“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… 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… 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.'” (John Piper)
For more on the subject, visit the Systematic Theology page.