The dove represents the Holy Spirit or the Holy Ghost in Christianity. The Holy Spirit descended upon Jesus like a dove when he was baptized in the Jordan River:
Luke 3:22
... and the Holy Spirit descended on him in bodily form like a dove. And a voice came from heaven: "You are my Son, whom I love; with you I am well pleased." (NIV)
The dove is also a symbol of peace. In Genesis 8 after the flood, a dove returned to Noah with an olive branch in its beak, revealing the end of God's judgment and the beginning of a new covenant with man.