Having participated in an Ifa sacrifice of some chickens and doves, the explanation given to me was that the animal spirit is a messenger from the material world to the spirit world. You tell the animal the message you want sent, it gets its neck wrung, and it carries the message to the other world. (I guess spirits don't accept faxes).
The animals are also used to 'feed' your spiritual protectors.
oh, and we plucked, cooked and ate the sacrifice afterward.
Tasted like chicken
...well, it was chicken.