Wiktionary
n. (context theology English) A Christian doctrine, one of the five points of Calvinism, stating that true believers in Jesus Christ's substitutionary atonement on the cross (the "saints") cannot relapse and are predestined to salvation.
Wikipedia
Perseverance of the saints (also referred to as eternal security as well as the similar but distinct doctrine known as "Once Saved, Always Saved") is a teaching that asserts that once persons are truly "born of God" or "regenerated" by the indwelling of the Holy Spirit, nothing in heaven or earth "shall be able to separate (them) from the love of God" (Romans 8:39) resulting in a reversal of the converted condition.
Sometimes this position is held in conjunction with Reformed Christian confessions of faith in traditional Calvinist doctrine which argues that all men are "dead in trespasses and sins" and so apart from being resurrected from spiritual death to spiritual life, noone chooses salvation alone.
Calvinists maintain that God selected certain individuals before the world began and then draws them to faith in His Son, Jesus Christ. They believe that when Jesus said, "No man can come unto Me except the Father which hath sent Me draw him" (John 6:44), Jesus was saying that men had to be drawn to Him by God before they would believe. Calvinists have long taught that when the apostle Paul wrote, "God hath chosen us in Him before the foundation of the world" (Ephesians 1:4), he was indicating that God actually chose believers in Christ before the world was founded. According to Calvinism, God begins a good work in some and then continues it. They attempt to prove that with the text from the book of Phillipians where the apostle Paul writes, "He which hath begun a good work in you will perform it until the day of Jesus Christ" (Philippians 1:6).
There are also many non-Calvinists who also maintain that a person who is saved can never be lost. This Free Grace or non-traditional Calvinist doctrine is found predominantly in "free will" Baptist theology, but also other Protestant churches of the evangelical tradition.
The doctrine of Perseverance of the Saints is distinct from the doctrine of Assurance, which describes how a person may first be sure that they have obtained salvation and an inheritance in the promises of the Bible including eternal life. The Westminster Confession of Faith teaches on Perseverance of the Saints in its Chapter 17 and on Assurance of Grace and Salvation in its Chapter 18.