This is definitely an anthropological rather than historical question, but since you are here:

Sacrifice (animal or otherwise) is one of the core ritual expressions of early human belief. It is a very basic manner of expression, joined by dance, song (hymn, chant, etc), visual media expression, prayer contract, competition/violence, ritual consumption (eating, drinking), and physical demarcation (including the setting aside of sacred space; procession to/from sacred space; and restriction of space, like location of burials).

Animal sacrifice is the very basic expression of loss of a valuable resource as demonstration of honor (to divinity), gratitude (for divinity), or request (from divinity). As such, the value of the sacrifice is proportional to the display: 100 bulls in Homer is of course much more weighty than a single goat. Of those core elements listed above, sacrifice is generally regarded as the most important and the "core" early religious expression--it is the "payment" to the god, and is a composite of a physical and speech act coupled with a prayer contract; the method of the sacrifice is like a dance in that it has choreography and ritualized action, there is an element of violence and an element of consumption (depending on the culture), and the act itself is physically demarcated by the slaying of the victim and its blood at the altar (or whatever required location), and the act itself is set apart from non-ritual action (like the slaughtering of a lamb for supper). By sacrificing the animal, you willfully destroy its value and therefore uphold the "contract" for the desired divine outcome, be it prowess in battle, fertile crops, good fishing, good sailing weather, a happy marriage or contract, punishment of a transgressor, etc. In short, the sacrifice indicates that you mean business in your expression.

Some societies found ways to optimize this act for their own benefit. The Greeks, cynically, worked out a myth (Prometheus) in which the less useful parts of the animal are sent as smoke to the gods, while the tasty bits remain left behind to be consumed by the performers. They have undermined the basic act of the sacrifice (the destruction of value) but normalized it through practice while still retaining the basic intent (brilliant, really). The Greeks have also subtly shifted the act towards consumption, in that the sacrifice begins to take on the aspect of an invitation to dinner, of communal dining with each other and the divine, and therefore the strengthening of bonds. Communal action is extremely important, nigh essential, to ancient ritual, and the Greeks cleverly integrated this impetus for communal consumption into the sacrifice ritual itself. The cynical reversal of no longer "losing" the value of the victim is compensated by the net gain of the ritual communal feast. It's fascinating.

Very early on, Greek authors shy away from the notion of a god "consuming" along with them, however. The gods are observers of the sacrifice and the communal feast, but not the participants, except in exotic circumstances (like Zeus feasting among the Aethiopians, who are separated spatially from the parameters of Greek ritual practice). The Homeric epics (probably first written down in the 8th century BCE, and therefore during the very formative period of Greek social behavior) tend to shy away from the carnal aspect of the gods "eating" the sacrifice as presented. Odyssey book 3 is famous for its detailed description of the sacrifice of a heifer (it is long so I won't put it here unless requested), and there, Athene attends the sacrifice of her ward Telemachos, but the language is specific: she "goes to meet" them as they sacrifice, but she does not consume what they offer--she only observes and presumably checks that things are done properly and with appropriate reverence and expense. In fact, the notion of a god consuming a sacrifice for his/her own nourishment or betterment is probably a gross misunderstanding of the origins of the ritual behavior: it is not the god's state or hunger or attitude at issue, but the state of the performer, who is necessarily lessened, harmed, impoverished by the act.

Lots and lots of work has been done on sacrifice. Typically it is centered on Greek practice, since the evidence is so good there, and comes from a lovely variety of archaeological, epigraphic, and literary sources. It's tough sledding, but one should probably start with Burkert (W. Burkert, Homo Necans, (Berlin 1972)). There is a rather recent volume called Animal Sacrifice in the Ancient Greek World which does things a little differently than Burkert (see here); and another classic study is M. Detienne – J. P. Vernant, La Cuisine du sacrifice en pays grec, (Paris 1979)