Actually, it doesn´t mean anything. Why? Should it? I just like the sharp contrast of red with white and I consider it an interesting picture, not that I like blood, of course.
The word "Avatar" in English comes from an old Hindu belief regarding gods inhabiting the bodies of mortals, to interact with humanity. Thus, an avatar is a means by which someone represents themselves with a chosen image in a situation where one would may otherwise be "faceless".
Hence, you'll find that most people here will choose an avatar that they feel represents them, or an aspect of their personality, etc.
I imagine this is why the good Magister asked about yours, as it seems an odd image to want to convey (as that kind of imagery is often used by disaffected youths wishing to represent their commonly self-inflicted pain in some fashion).