This depends on which ancient cultures you're asking about. I can tell you a bit about Ancient Greek sacrificial practices, though! This source describes the origin of Greek sacrificial practices: a titan named Prometheus created humans, but Zeus demanded that humans sacrifice their animals to the gods. Prometheus got Zeus to agree to allow the humans to keep part of the animal for themselves.

"Prometheus knew that Zeus wanted all the good parts of the animal and came up with a plan to trick him. Prometheus took an animal and divided the choice cuts of the meat from the bones and other less savory tissues. On the pile of bones, he placed fat and a small portion of nice meat on top to disguise it, but on the pile of good meat he placed some lesser meat and gristle."

(Prometheus then stole fire and gave it to humans, and was severely punished by Zeus).

As far as archaeological evidence of this practice goes, this article discusses the remains of feasts at the Palace of Nestor in Pylos. It states that "several deposits of faunal remains appear to be the remnants of burned animal sacrifices made on a single occasion and of the consequent distribution of meat to a large number of individuals," indicating that feasts and sacrifice went hand-in-hand. This makes sense: in Ancient Greece (and even now in modern Greece), the concept of xenia/ξενια, which is often described as "guest-friendship" was one of the core societal values. It was kind of like hospitality on steroids. If you've heard of the Trojan War, it began when Paris was a guest of Menelaus, and then ran off with Menelaus's wife. This is a dick move to begin with, but particularly bad because Paris violated guest-friendship.

Throughout almost all cultures, sharing food is a bonding ritual. So in Ancient Greece, this practice of sacrificing to the gods and distributing the food acted as a way of cementing social ties.