These five points of doctrine lay out God’s sovereign work in the redemption of man. His sovereignty is the overarching truth. It is all His work alone. That is the essence of what is termed Monergism. In brief, in my own woefully inadequate words, the five points can be summarized as follows:

Total Inability (or Depravity)
As a fallen being, all persons are by nature part of the world and seek the world rather than God. Their worldview is world-centered putting them at enmity with God. As such, they are incapable of turning truly to God. They would not want to. They are totally unable.

Unconditional Election
Before the creation of the world, God chose who he would subsequently save through His gracious intervention. This was done before they existed in human form and before they could accomplish anything, either good or bad. This election was by God alone for His own divine reasons.

Limited (Particular) Atonement
By serving as a substitute through His death, Jesus Christ atoned for the sins of the elect. He provided a path to justification before God for those who, by virtue of their inherent sinful nature, could not do so for themselves. Christ, as God, could not fail in this process. As such, although Christ’s atonement was infinitely sufficient, it could only apply to the elect. A universal application would mean that He had failed in those who do not believe.

Irresistible Grace
This refers to God’s grace in salvation. God, through the work of the Spirit, graciously regenerates the elect individual. Regeneration is accomplished by the Spirit at the spiritual level. It occurs before faith and while the individual is still of the world and at enmity with God. Since it is the work of God, it is always accomplished and always successful. God is sovereign. Since the regenerated person is then oriented toward God, faith in Christ is the natural (actually the only) choice and is assured. Thus, salvation is assured.

Perseverance of the the Saints
The life-long sanctification that follows conversion is under God’s sovereign will. As such, irrespective of life’s situational difficulties (prolonged and severe as they may be), the redeemed will be sanctified by the end of their lives. As Jesus states in John 10:28 “I give them eternal life, and they will never perish; and no one will snatch them out of My hand.”

For a more complete, and certainly more competent, exposition of this all important doctrine, I would strongly recommend The Doctrines of Grace by James Boice, and The Five Points of Calvinism by Steele. The Boice book is particularly cogent.