Irresistible grace is that sovereign, all-powerful work of the spirit in the soul of an elect sinner—that sweetly allures and graciously enables that sinner to want to come to Jesus Christ for salvation – John 6:37,44
John Piper – ‘The doctrine of irresistible grace means that God is sovereign and can overcome all resistance when He wills… 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.’ – http://www.desiringgod.org/articles/what-we-believe-about-the-five-points-of-calvinism#Grace
* See; Attached PDF outline