The Latin Cross, is the basic Christian cross that almost everyone recognizes. It may surprise many people that, like most crosses, this was originally a pagan symbol, and is found in many prechristian cultures. Prior to the adoption of this symbol Christianity was most often represented by symbols like the Fish and Chi-Rho.
The cross was the device used to execute Jesus, the founder of Christianity. Christians believe that his execution was actually an act of self sacrifice on behalf of Jesus, to atone for the sins of the world. The cross was adopted in the 6th or 7th century as an reminder of that event and a symbol of Christianity.