The dove is the symbol of peace, as well as the Holy Spirit.

As a peace symbol it recalls the Arc of Noah.

Gen. 8:10-11. "He waited another seven days, and again he sent out the dove from the ark; and the dove came back to him in the evening, and there in its beak was a freshly plucked olive leaf; so Noah knew that the waters had subsided from the earth. "

 

The dove is a symbol of the Holy Spirit, the third person of the Trinity, because of Matt. 3:16 "And when Jesus had been baptized, just as he came up from the water, suddenly the heavens were opened to him and he saw the Spirit of God descending like a dove and alighting on him. " NRSV. [See El Greco's Baptism.]