@windwhistler :
"Irresistible Grace" teaches that when the Gospel is preached ( Romans 10:8-21, 1 Corinthians 1:18-31, ), only those who have "ears to hear" ( Matthew 11:27, Matthew 13:9 and many others, including John 8:43-47 ) willingly receive God's words and believe them "to the saving of the soul"...
Because faith "comes by hearing, but
hearing comes by the word of God" ( Romans 10:17, Do you see the subtle difference? Faith coming
by hearing, placing it on man to do the act under "Prevenient Grace", versus faith coming
by hearing, but
hearing coming
by the word of God, placing it on God to do the act ).
They are God's elect, a remnant out of every tongue, tribe and nation ( and a multitude which no man can number, see Revelation 5:9 and Revelation 7:9 ) whom the Lord has graciously chosen, in His wisdom, to have mercy and compassion on ( Romans 9:13-24 ).
The rest will invariably reject God's words because they are not "of God", or they will "believe" for a time and then fall away because they are "tares", sown in Christ's "field" by His enemy, the devil ( Matthew 13:24-30, Matthew 13:36-43 ).
All who are the Lord's elect, chosen in Christ from the foundation of the world, will be kept and not one of them will be lost.
God's foreknowledge is said to be active in this sense, and it is described not only as knowing
about His people, but intimately knowing ( loving ) them, in His mind's eye, before they were born ( Jeremiah 1:5, Psalms 139 ).
God's decision to save someone was made independent of what we do as men, and belief of His words necessarily
follows as a result of God's miracle of the new birth.
Sometimes referred to as "Calvinism", this set of teachings ( there's much more to it than simply "Irresistible Grace" ) will never see one of God's precious children fall away...even under often terrible trials and tribulations in this life.
They not only are kept by His own power ( 1 Peter 1:5 ), they are truly born again and sealed by the Spirit of God until the day of their bodily redemption.
This includes regeneration
before faith, with God's gifts of eternal life, righteousness in His sight and the understanding of the Scriptures relying, at their foundation, on God's efforts alone on the behalf of those He has decided to save.
I hope that helps, and may God bless you in your studies.