I actually made a post on this a while back, on another forum.
In today's society, the act of sacrifice is looked upon with confusion, ire, or misconception and pacification. With the later, we see things being called a "sacrifice", when it's something trivial and non-committal as "I'm giving up drinking soda for a whole week."
Sacrifice, in the purest of terms, is the act of giving something up for good. For this reason, animal sacrifice (or even blood sacrifice) is among the greatest acts of sacrifice to an ása. They are sacrifices in that once the life is given, it cannot be reclaimed. It is not a loan or casual discard; it is a serious and impacting loss of assets, life, or even time and effort, given with the intent of full claim on end of the Æsir.
With animal sacrifice, one is giving up one of your livestock in honor to an ása, either to petition for easy weather or simply as a gesture of fealty. For petitions, a positive result is not guaranteed.
Hunting can also be seen as a form of animal sacrifice, though it follows a different theme. Rather than you giving up one of your animals, the hunter acknowledges their claiming of both an individual life, and a life under guardianship of an ása or vættir. Rather than giving a full sacrifice, we honor and recognize a sacrifice that we have taken, and a portion of that claim is given back in thanks to the Æsir or vættir. This same form of sacrifice is utilized for things such as crop harvest and lumbering.
With blood sacrifice, an individual gives a portion of their blood for a given end, usually for wards or forms of seðir that involves crafting. While the body regenerates blood naturally, the act is still a sacrifice in that you have given a part of yourself that you won't get back for a given purpose. What's more, blood sacrifice (or blood magic) is seem as powerful through proper in that your essence (and your wyrd) is now tied to the object or intent that you have made. Sometimes such a sacrifice is taken by the Æsir, without us giving it--small cuts or such in the crafting of an object.
Sacrifices are also given on the small scale. When we make a meal, especially at large gatherings, a portion of the good is given to either a particular ása, our to the land vættir in general. Alcohol - typically mead - is often given as a sacrificial offering to the Æsir or vættir on blóts or simbuls.
Glossary
●Ása (plural Æsir): A god, feminine being ásynja (pl. ásynjur). Though two tribes - the Æsir and Vanir - they are collectively referred to as Æsir--similar to "mankind".
●Vættir: Spirits, of either men or the land.
●Blót: A small ritual or dedication.
●Simbul: A more serious and sacred ritual, e.g. those that would be held at a temple.
●Wyrd: Fate, pronounced "weird".