Preface: words in brackets required special characters
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/human sacrifice) is among the greatest acts of sacrifice to an [as] . 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 Aesir.
With animal sacrifice, one is giving up one of your livestock in honor to an [as] , 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 [as] or vaettir. 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 Aesir or vaettir. 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 sedhir 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 (our blood magic) is seen as powerful 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 Aesir without us giving it--small cuts or such in the crafting of an object.
Human sacrifice is, by far, the more controversial - and vilified - forms of sacrifice that has existed (and still does exist) in the past. Typically, in ancient Norse culture, human sacrifice was given of the types of people: criminals, or those captured during war; thraell of a king, queen or jarl; the common man or warrior.
With the later two, the sacrifice was strictly a voluntary act. Thraell could choose to follow their king, queen or jarl into the afterlife, continuing their service to him or her. The common man (or woman) could give of their life to defend their kin - a sacrifice to their people - or give their life to the Aesir for a given purpose.
For those captured during war, or for criminals of heinous crimes (such as murder,) the sacrifice of their life was not an option for them. They were given to the Aesir, as either evidence of victory or as evidence of justice.
Our views on human sacrifice play a pivotal role in the view of the Sacrifice of Odin, in that to grasp the magic of the runes, Odin sacrificed his godhood to become mortal. As such, he sacrificed his life for higher knowledge, dying and being reborn as an [as] again. He gained an experience, and simultaneously lost an experience and being twice over.
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 [as] , our to the land vaettir in general. Alcohol - typically mead - is often given as a sacrificial offering to the Aesir or vaettir on blots or simbuls.
Glossary
[As] (plural Aesir): A god, feminine being [asynja] (pl. [asynjur] ). Though two tribes - the Aesir and Vanir - they are collectively referred to as Aesir--similar to "mankind".
Vaettir: Spirits, of either men or the land.
Blot: A small ritual or dedication.
Simbul: A more serious and sacred ritual, e.g. those that would be held at a temple.