Birds are also well known with the element Air. This element rules over the mind, and represents our thoughts. Air was believed in many cultures to carry the smoke from our prayer candles to the Heavens, so they may be heard. I view air as a counterpart element to water (as it is within it), and fire (as it feeds it).
The pigeon may represent your thoughts being clouded, or even developing. Maybe you have to let go of something, and it is telling you that you may release it, and the pigeon will take it away in a sense.
I have a friend who believes each person has three Spirit Animals; One that sticks with them their whole life, who that represents their biggest fear, and one that changes as they go through stages of life. The pigeon may not be your permanent spirit animal, so keep that in mind also :))