A blessing is a prayer asking for divine protection, or a little gift from the heavens. It's also any act of approving, like when your roommate wants to move out and you give her your blessings.
Blessings have to do with approval. The first meaning is asking for divine protection or favor. Priests and ministers say blessings in church, and some families say a blessing before dinner. Outside a religious context, blessings are less formal. "I give you my blessing" simply means "It's OK with me." People give their blessings to ideas and actions when they agree with them. Giving a blessing is often the same as giving permission.