Sacrifices have been made for various reasons, but for the most part they fall into four categories: releasing attachment, in reverence/celebration of gods, to build energy, and to return the energy given by the universe/gods.
In many magickal systems there is a need to release the attachment or memory of a ritual or spell in order for it to work. This is primarily based on the idea that you continue to draw energy from that spell every time you think of it or talk about it, thus weakening the spell. A very common way to do this is through a sacrifice. This is commonly done by taking the ashes of a ritual fire and burying them, burning something, throwing an energized object into a forest, etc. It is almost always some sort of material sacrifice that happens at the very end of the spell or ritual as a closing. I’m not really sure why this works, but it is one of the best ways to break the attachment from the spell. Maybe this is something that we could discuss some more.
Every religion/culture has made sacrifices to celebrate or revere the gods or spirits that they associate with. Some of the examples could be the ritual human sacrifices by the Aztecs, the sacrifice for Lent by Catholics, or even when warriors would pour out the first bit of a drink for their fallen comrades. This is as much to give reverence to the gods and spirits as it is to bring out the emotions necessary for that celebration. The Aztec human sacrifices were a way to call forth the energy of Huitzilopochtli, the sun god, as well as put everyone there in an emotional state to welcome that energy into their lives; that’s not even mentioning the energy that Huitzilopochtli received for each of these sacrifices (they did become an incredibly large empire, maybe this had something to do with it?) There is a lot more to this ritual because it was such a serious sacrifice, but that’s the most important part of it in my opinion. The sacrifice that people make for Lent is a way for people to build up the martyr energy necessary to understand what Easter and Lent are all about. It is also a way to celebrate Jesus’s personal sacrifice made to his followers. The warrior’s sacrifice is different than these because it is obviously more about bringing forth the emotional response of remembering loved ones and celebrating their lives. It is also to remember that we are all mortal and that we should enjoy ourselves. All of these sacrifices give energy to the spirit that is deserving of the sacrifice and gives them power, but it also allows the energy that they are giving to come into their lives through the emotional response of the sacrifice.
As Jessica stated, there is a common idea in many cultures that requires a gift be returned with something worth at least equal value. Therefore, gifts were often more of obligations than gifts. The Norse have a rune called Gebo that signifies this idea as a gift that must be returned or honor and status are lost. Therefore, if you sacrifice something to a god, they are obligated to give you something in return and vice versa. Therefore, a safe voyage on the sea required a gift to the gods of the sea or else they would be angry because the “gift” of safe passage was not returned in equal value. This can also be seen at Christmas time in modern America when people give the most they can afford in order to maintain or achieve a higher status in the family.
I’m sure that I’m missing some categories, but these were the only ones I’ve been able to come up with. I guess that you could categorize spells as well, but these seem pretty clear cut as far as divisions go.