The doctrine of irresistible grace does not mean that every influence of the Holy Spirit cannot be resisted. It means that the Holy Spirit can overcome all resistance and make his influence irresistible.
In Acts 7:51 Stephen says to the Jewish leaders, "You stiff-necked people, uncircumcised in heart and ears, you always resist the Holy Spirit as your fathers did." And Paul speaks of grieving and quenching the Holy Spirit (Ephesians 4:30; 1 Thessalonians 5:19). God gives many entreaties and promptings which are resisted. In fact the whole history of Israel in the Old Testament is one protracted story of resistance, as the parable of the wicked tenants shows (Matthew 21:33-43; cf. Romans 10:21).
The doctrine of irresistible grace means that God is sovereign and can overcome all resistance when he wills. "He does according to his will in the host of heaven and among the inhabitants of the earth; and none can stay his hand!" (Daniel 4:35). "Our God is in the heavens; he does whatever he pleases" (Psalm 115:3). When God undertakes to fulfill his sovereign purpose, no one can successfully resist him.
This is what Paul taught in Romans 9:14-18, which caused his opponent to say, "Why then does he still find fault? For who can resist his will?" To which Paul answers: "Who are you, O man, to answer back to God? Will what is molded say to its molder, 'Why have you made me thus?' Has the potter no right over the clay, to make out of the same lump one vessel for beauty and another for menial use?" (Romans 9:20f).
More specifically irresistible grace refers to the sovereign work of God to overcome the rebellion of our heart and bring us to faith in Christ so that we can be saved. If our doctrine of total depravity is true, there can be no salvation without the reality of irresistible grace. If we are dead in our sins, totally unable to submit to God, then we will never believe in Christ unless God overcomes our rebellion.
Someone may say, "Yes, the Holy Spirit must draw us to God, but we can use our freedom to resist or accept that drawing." Our answer is: except for the continual exertion of saving grace, we will always use our freedom to resist God. That is what it means to be "unable to submit to God." If a person becomes humble enough to submit to God it is because God has given that person a new, humble nature. If a person remains too hard hearted and proud to submit to God, it is because that person has not been given such a willing spirit. But to see this most persuasively we should look at the Scriptures.
In John 6:44 Jesus says, "No one can come to me unless the Father who sent me draws him." This drawing is the sovereign work of grace without which no one can be saved from their rebellion against God. Again some say, "He draws all men, not just some." But this simply evades the clear implication of the context that the Father's "drawing" is why some believe and not others.
Specifically, John 6:64-65 says, "'But there are some of you that do not believe.' For Jesus knew from the first who those were that did not believe, and who it was that should betray him. And he said, 'This is why I told you that no one can come to me unless it is granted him by the Father.'"
Notice two things.
First, notice that coming to Jesus is called a gift. It is not just an opportunity. Coming to Jesus is "given" to some and not to others.
Second, notice that the reason Jesus says this, is to explain why "there are some who do not believe." We could paraphrase it like this: Jesus knew from the beginning that Judas would not believe on him in spite of all the teaching and invitations he received. And because he knew this, he explains it with the words, No one comes to me unless it is given to him by my Father. Judas was not given to Jesus. There were many influences on his life for good. But the decisive, irresistible gift of grace was not given.
2 Timothy 2:24-25 says, "The Lord's servant must not be quarrelsome but kindly to every one, an apt teacher, forbearing, correcting his opponents with gentleness. God may perhaps grant that they will repent and come to know the truth."
Here, as in John 6:65 repentance is called a gift of God. Notice, he is not saying merely that salvation is a gift of God. He is saying that the prerequisites of salvation are also a gift. When a person hears a preacher call for repentance he can resist that call. But if God gives him repentance he cannot resist because the gift is the removal of resistance. Not being willing to repent is the same as resisting the Holy Spirit. So if God gives repentance it is the same as taking away the resistance. This is why we call this work of God "irresistible grace".
NOTE: It should be obvious from this that irresistible grace never implies that God forces us to believe against our will. That would even be a contradiction in terms. On the contrary, irresistible grace is compatible with preaching and witnessing that tries to persuade people to do what is reasonable and what will accord with their best interests.
1 Corinthians 1:23-24 says, "We preach Christ crucified, a stumbling block to Jews and folly to Gentiles, but to those who are called, both Jew and Greeks, Christ the power of God and the wisdom of God." Notice the two kinds of "calls" implied in this text.
First, the preaching of Paul goes out to all, both Jews and Greeks. This is the general call of the gospel. It offers salvation to all who will believe on the crucified Christ. But by and large it falls on unreceptive ears and is called foolishness.
But then, secondly, Paul refers to another kind of call. He says that among those who hear there are some who are "called" in such a way that they no longer regard the cross as foolishness but as the wisdom and power of God. What else can this call be but the irresistible call of God out of darkness into the light of God? If ALL who are called in this sense regard the cross as the power of God, then something in the call must effect the faith. This is irresistible grace.
It is further explained in 2 Corinthians 4:4-6, "The god of this world has blinded the minds of unbelievers, to keep them from seeing the light of the gospel of the glory of Christ, who is the likeness of God...It is the God who said, 'Let light shine out of darkness,' who has shone in our hearts to give the light of the knowledge of the glory of God in the face of Christ."
Since men are blinded to the worth of Christ, a miracle is needed in order for them to come to see and believe. Paul compares this miracle with the first day of creation when God said, "Let there be light." It is in fact a new creation, or a new birth. This is what is meant by the effectual call in 1 Corinthians 1:24.
Those who are called have their eyes opened by the sovereign creative power of God so that they no longer see the cross as foolishness but as the power and the wisdom of God. The effectual call is the miracle of having our blindness removed. This is irresistible grace.
Another example of it is in Acts 16:14, where Lydia is listening to the preaching of Paul. Luke says, "The Lord opened her heart to give heed to what was said by Paul." Unless God opens our hearts, we will not heed the message of the gospel. This heart-opening is what we mean by irresistible grace.
Another way to describe it is "new birth" or being born again. We believe that new birth is a miraculous creation of God that enables a formerly "dead" person to receive Christ and so be saved. We do not think that faith precedes and causes new birth. Faith is the evidence that God has begotten us anew. "Every one who believes that Jesus is the Christ has been born of God" (1 John 5:1).
When John says that God gives the right to become the children of God to all who receive Christ (John 1:12), he goes on to say that those who do receive Christ "were born, not of blood nor of the will of the flesh nor of the will of man, but of God." In other words, it is necessary to receive Christ in order to become a child of God, but the birth that brings one into the family of God is not possible by the will of man.
Man is dead in trespasses and sins. He cannot make himself new, or create new life in himself. He must be born of God. Then, with the new nature of God, he immediately receives Christ. The two acts (regeneration and faith) are so closely connected that in experience we cannot distinguish them. God begets us anew and the first glimmer of life in the new-born child is faith. Thus new birth is the effect of irresistible grace, because it is an act of sovereign creation -- "not of the will of man but of God."
** Excerpt Taken From What We Believe About the Five Points of Calvinism by John Piper & Bethlehem Baptist Church Staff