The Cross
The cross is the main symbol of Christianity.  It reminds Christians that Jesus died on the cross for their sins.

The Dove
The symbol of the dove represents peace and the Holy Spirit.

The Fish
The fish symbol was created using the Greek letters which spell out ICTHUS.  When the Romans started persecuting Christians, the fish symbol was used by Christians upon meeting.  One person would draw half of the fish and the other person would draw the other half.  This allowed them to identify themselves as Christians and know if the person they were talking with was also a Christian.