Origin of the practice

Humans are god fearing in nature. In almost every religion there is a belief that sacrifices are made by humans to appease god(s). Hence, to make amends of past sins, or to get god's blessings or to express thankfulness, humans offer certain things as sacrifice to god(s). Anything of some value may be considered as a thing of sacrifice in some religion's practices. The more valuable the offering, the more highly the sacrifice is regarded and certainly more difficult to make. Commonly, the most valuable sacrifices have been that of lives --- livestock (i.e. animals) and humans.

Inner meaning behind such practices

Among all these types of sacrifices, animal sacrifice is the most common form. Earlier, animals were not regarded inferior to men; on the contrary, they were often regarded as divine beings. There is a deeper meaning behind animal sacrifice. Animal sacrifice it seems did not take place just to appease Gods, it was a way for atonement for one's sins. Animal sacrifice was considered fit for the atonement of human sin as it was the human being in question who disregarded his elevated human soul and acted like an animal then.

Besides humans, considered as the best creation of God, offered as a sacrificial object could be the best gift that a worshipper could offer to his or her god. The act also shows the desire to shift the blame, to find some person or even object that can be held guilty and punished for an act which, nevertheless, was regarded as an essential observance, the omission of which would bring disaster upon the state.
Hence, in ancient times, those who were captured as prisoners of war were often sacrificed in front of god(s) by the victorious as a token of thanks in return of the victories that were made possible by the grace of god(s).

Sacrifice can be bloodless too. For example the food, drinks and other innate artifacts that are offered to god(s) are also considered as sacrifices made by the worshipper. The act of sacrifice is again an act of detachment practiced by the worshipper or for some it could be a selfish act of donation with wish for greater returns and benefits.