Calvinism is a series of beliefs based on those of John Calvin and his followers.  Calvinism has five points to it which spells out the acronym TULIP.  Those who believe in all five points may be considered five point Calvinists.  Others may consider themselves three point Calvinists while others who only believe in the preservation of the saints may consider themselves a one point Calvinist.

The Arminian view is considered the alternative to the Calvinistic view.  While there are many who consider themselves strictly Arminian or Calvinist, there are others who claim to be somewhere in between.

The five points of Calvinism were not created by Calvin but rather originated at the Synod of Dort in 1619.  It was a response to the five points of the Arminian Remonstrance in 1610 (which was a response to Calvin's ideas.)

Five points of Calvinism:

Total Depravity

Unconditional Election

Limited Atonement

Irresistible Grace

Perseverance of the Saints

For more information, see the articles Calvinism Basics and Arminianism vs. Calvinism.