Calvinists today have started using the term Effectual Calling in the place of what older Calvinists called Irresistible Grace, this is probably a smart move for this latter term often conveys a false understanding of what is meant.
This is for various reasons, but I think Jonathan Edwards explained it best. In the first few chapters of his Freedom of the Will he defines the terms he will be using later in the book, one of the terms defined was Irresistible. With the words Necessity and Impossibility Edwards separated the colloquial (or proper/general) use of these words from the philosophical (or “arts”) use of the word. 
In common speech “irresistible” means that something will come to pass no matter how much one may resist it. It demands the possibility, even the necessity, of resistance in its very meaning. When a Calvinist says that they believe in Irresistible Grace the natural tendency is for one to assume that the person will come to Christ against their will, it is a grace forced upon someone that batters down all resistance and leads inevitably to salvation. While some Calvinists have taught Irresistible Grace in this manner, this is not a good description of what the Bible teaches, nor of how most Calvinists present the Biblical teaching.
Effectual Calling bi-passes this unfortunate misunderstanding by using language that accurately reflects what Calvinists mean when they speak of Irresistible Grace; it is a calling made by God to His elect that will always be effective, it will never fail to bring about the end of saving faith.
Irresistible Grace is useful as part of the mnemonic acronym TULIP, it is useful as a tool for teaching the basics of what Calvinists call the Doctrines of Grace; but this pro is dramatically outweighed by the con of inaccuracy. The Calvinist understanding of Scripture is already misunderstand by many, some within its own camp, and we should do our best to describe it in a way the best conveys the true essence of the doctrine, even if it is less memorable.
Some may still think; if the Effectual Call brings around a certain effectual result, doesn’t this also in its name imply the very issue that Irresistible Grace does; if our response to God’s call is guaranteed then we are not free in expressing faith but are coerced.
As I have studied the Doctrines of Grace I have come to realize that one of the foundational differences between Arminianism and Calvinism is a disagreement between what it means to be free; they both take a different position on what it means for mankind to make meaningful choices for which a man or woman can be held responsible. See the glossary from my paper on Hell here for further definitions, but in a nut-shell; Calvinists conclude from the testimony of Scripture that the outcomes of a choice can be rendered certain (determined any time in the past) and yet we still are rightly held responsible for our choices and they are meaningful choice (some, like Edwards, call this freedom, others, like Luther, reject the word freedom because of its predominate association with Incompatibilism), this position is called Compatibilism (Determinism—the rendering certain of future choices—is compatible with humans making meaningful choices for which they are responsible); Arminians assume from the start that to be free we must have the freedom to choose from alternatives, we must be able to choose option A or Not-A at all times; this is a position called Incompatibilism, which says that determination is incompatible with meaningful human choices—i.e. if the outcome of a choice is rendered certain then that choice was not free. Whereas the term Irresistible Grace implies coercion, which both positions agree negates free choices, the term Effectual Call refers to the end result being guaranteed; this is something that Calvinists understand to be completely compatible with meaningful human choices for which we can be held responsible.
Irresistible Grace is a misnomer not just because of this confusion over terminology, but also because it doesn’t quite capture the essence of the doctrine as well as Effectual Call; what exactly do Calvinist’s mean when they speak of Irresistible Grace or the Effectual Call?
The “I” in TULIP states that God will work a change in the hearts of His elect people so that they will no longer hate Him and reject His reality—which they are suppressing in their unrighteousness (Rom. 1:18-32)—but joyfully and willingly respond to His general call brought through the preaching of the Gospel. The Effectual Call is God’s regenerating work in the hearts of His elect people that overcomes their depraved nature with the creation of a new heart and without fail brings them to saving faith.
In Romans 8:28-30 Paul writes to the Romans about God’s work in His people, he promises that “God causes all things to work together for good to those who love God, to those who are called according to His purpose.” The reason Paul confidently writes that we know this is because (οτι, hoti; for, v. 29) everyone whom God foreknew He also predestined for salvation,  and this same group—that is everyone whom He first foreknew and then predestined to become conformed to Chris—He will call, and everyone in who is called in this sense will respond (30). This call is cannot be the general call delivered to all mankind through the preaching of the Gospel (cf. Matt. 22:14), for we know that not everyone responds in saving faith; this is different call which ensures a salvific response, what Calvinist’s call the effectual call.
One of the many verses (cf. John 3 for another example) Calvinists use to defend this doctrine and to suggest that this call is regeneration is John 6:44-46. Here Jesus responds to grumbling of the Jews about what He has been teaching (that He is the bread of life), He responds; “44“No one can come to Me unless the Father who sent Me draws him; and I will raise him up on the last day.45“It is written in the prophets, ‘And they shall all be taught of God.’ Everyone who has heard and learned from the Father, comes to Me.”” In this text Jesus says that it is necessary for God to draw someone if they are to come to Him, he then goes on to explain what exactly this “draw” entails. First He says that all who are drawn will be resurrected on the last day, the context implies not just a general resurrection to either Heaven or Hell but a salvific resurrection; they will be glorified. This indicates that not all are being drawn, especially since Jesus gives this explanation to explain why some Jews do not believe, and that everyone who is drawn will effectually respond in saving faith (which is the only way anyone will be glorified, for we are saved by faith) (v. 44c). Jesus then goes on to explain what this drawing is from an Old Testament text, the verse in question is Isaiah 54:13. This is a promise of the New Covenant, specifically a promise of the new hearts given to those under the New Covenant. Under the Old Covenant Israel had an issue, they were a mixed community; within the Covenant community there was a remnant that was regenerate, that is they obeyed God, but the majority of Israel was made up of covenant breakers, that is; those who did not keep God’s covenant with them. As early as Deuteronomy we see the need for a change, the need for what will later be called the Covenant of Peace or the New Covenant. In Deuteronomy 29:5 we read that the Lord had not yet given the people a heart to believe and follow Him, in 30:6 Moses speaks of a time when God will circumcise the hearts of the Israelites in order that they may obey Him; they needed this circumcision of their hearts because they were unable on their own to be obedient, they were depraved. Throughout the rest of the New Testament we see various promises of a New Covenant in which every member of the Covenant would be enabled to obey God by the gift of a new heart; they all would be taught by God, God’s law would be written on their hearts and minds, they would have new and circumcised hearts (Jeremiah 31:33-34, Ezekiel 36:22-38, and Isaiah 54; cf. Hebrews 8); these prophecies all find their culmination in the regeneration experienced by all New Testament believers. On the cross Jesus ushered in this New Covenant (Luke 22:20). Jesus hear in John 6:45 is saying that the drawing of the Father is this New Covenant promise of regeneration and that everyone who has received this drawing, that is all that have “heard and learned from the Father,” will come to Him. This calling is effectual and it ensures a willing response of faith to the Gospel; in this text (including its greater context starting at v.22) God’s sovereignty in salvation, both Unconditional Election and the Effectual Call, are held up side-by-side with a willing response of faith to the Gospel; they are held up side-by-side but Jesus nor John sees a contradiction.
This is what Calvinists mean when they speak of Irresistible Grace, but it is much better represented by the term The Effectual Call. The Effectual Call is God’s regenerating work in the hearts of His elect people that overcomes their depraved nature with the creation of a new heart and without fail brings them to saving faith. And it would be wise for use, with Jonathan Edwards, to abandon the language of Irresistibility and use more accurate language of Effectual.
 I demonstrate this assertion from various Arminian works in a large paper and/or book that I am currently working on and hope to finish by the end of the year. In it I attempt to show as part of my larger argument—from books such as Arminian Theology, Classical Arminianism, Against Calvinism, and Chosen But Free—that an a-priori commitment to Incompatibilist Free Will leads inevitably to an Arminian theology and forms a foundational presupposition to their worldview and arguments.
 I know some will be offended by this choice of words, but most Arminians I read are unashamed of this presuppositions; see my upcoming paper/book on Prevenient Grace for a defense and explication of my view that this assumption is foundational to Arminian theology and can only be proven from the Bible if you first assume it (even then I would argue, and do in that paper, that you are forced to read the text in unnatural ways to accommodate this assumption).
 There are few different positions on what this specific call is, but the position I take is that it is regeneration. For an explanation of this position see; Wayne Grudem, Systematic Theology: An Introduction to Biblical Doctrine (Leicester; Grand Rapids, MI: Inter-Varsity Press ; Zondervan, 1994), 699–706.
 for the progression of our conformity to Christ starting with the legal declaration of our justification, progressing through the Spirit’s work of sanctification making us holy in nature, and concluding in glorification when our sanctification will be completed and we will sin no longer. See v.28-39.