A deer’s antlers may represent spiritual superiority. Like a crown, the antlers grow beyond the body of the deer, bringing it closer to the sky and therefore making it sacred. In many cultures, the deer is a symbol of spiritual authority. During a deer’s life the antlers fall off and grow again, and the animal is therefore also seen as a symbol of regeneration.
In Christian iconography, the deer appears as a symbol of piety, devotion, and is used to symbolise God taking care of his children. The legend of St Eustace, for example, tells the story of the Roman general Placido who, before becoming a saint, was out hunting and came across a magnificent, enormous deer. When Placido looked at the animal’s eyes, the light of Christ shone out of them and the voice of God spoke to him through them. Placido, gave up hunting and became a Christian, becoming famous as St Eustace.
In the Celtic tradition there were two aspects of the deer: the feminine element, called Eilid in Gaelic, the female red deer, symbolizing femininity, gentleness and grace. It was believed that the deer called to men from the kingdom of the fairies to free them from the trappings of the earthly world and take them to the world of magic. Deer often turned into women in such legends in order to avoid being hunted. On the other hand, there was also Damh, the masculine element, which was also related to the sacred and to forests, independence, purification and pride. The stag is the king of the forest, the protector of all other creatures.
http://www.faena.com/aleph/articles/notes-on-the-symbolism-of-deer/