What It Is (according to Me)
From my experience:
Asatru is a form of paganisms based on the Northern European Myths (IE Odihn, Thor, Frigga, Fryeja) Unlike most paganism, the beliefs are not stressed so much as the way of life. Culture, community, and especially family are the central focuses of most practitioners. Some practitioners are "gifted" in the arts of communicating with the gods but it is not important to the practice of the religion.
There are a lot of race controvercys associated with asatru (mostly because of hitler)
Some believe that this culture is the "Aryan race" and superior to everybody else.
Some people believe the cultures should remain separate, not because they are better than one another but because celebrating the culture is essential to ones heritage, and mixing it up has proven to "lose" knowledge that can never be returned.
Others believe that anyone can be called (and that is me BTW) by the Gods to serve.
There is only one primary text remaining of Asatru since the spread of Christianity(The Eddas). It has been translated and interpreted MANY ways. Because of this there is no set belief system and/or dogma, everybody is encouraged to read it and interpret it as they see fit. I find even when in a room full of Asatru practitioners (even those who commonly worship together) they have varying ideas of morality, dogma, and religion in general.