What Calvinists believe may be summarized from the five points of the Synod of Dort (1619). A popular acronym for the five points is "tulip." Each letter stands for one of the points. T is for total depravity. U is for unconditional election. L is for limited atonement. I is for irresistible grace. P is for perseverance of the saints.
Total depravity teaches that the fall of Adam brought all of humanity into a condition of sin. Man is unable to save himself. Many who are not Calvinists would agree with this point (Romans 3:10; 3:23). All mankind is in a state of spiritual death outside of Christ (Ephesians 2:1).
Unconditional election teaches that God chose only certain people to be saved before the world began. Their salvation is guaranteed by God's choice alone. It is unconditional, because it is not based upon anything that they could do. Those who are not chosen are simply left in their sins to perish. In essence, they are lost because God did not choose them.
Limited atonement teaches that Christ did not die to save all people. His death was designed to save only those whom God chose before the world began. These are the elect. All whom God chose, and Christ died for, shall be saved. Those who were not chosen cannot be saved, because Christ did not die for them.
Irresistible grace teaches that God makes the chosen ones willing to be saved. Their response to the call of God is certain, because God makes them willing. Those who cannot be saved are lost forever, because God chose not to make them willing.
Perseverance of the saints teaches that those whom God has chosen, for whom Christ died, are saved and can never be lost again. They are saved and persevere, because God chose them and not others. This is not to be confused with the doctrine of eternal security, taught by many who are not Calvinists. The basic reason for using the term eternal security is to not identify with those who believe in unconditional election, limited atonement and irresistible grace.
There are different groups among Calvinists. This includes moderate Calvinists and hyper-Calvinists. Moderate Calvinists are primarily those who do not accept the teaching of limited atonement. Often, they are referred to as four point Calvinists. Hyper-Calvinists believe all five points, but they do not believe in missions and evangelism.