What's super cool about the asexual movement is how they've raised awareness about multiple different types of attraction. See this website for a thorough explanation of sexual orientation, romantic orientation, and attraction types. That same page also has further links to resources that have tons more information, if you're interested. Be aware!
If you want a quick and extremely adorable explanation, see this post.
Also, look at this flag.
The best thing you can do to celebrate Asexual Awareness Week is to share information, and remember to correct people who don't understand. Remember that asexuality in humans has nothing to do with methods of reproduction, and there is nothing wrong with being asexual! As much as non-asexual people might enjoy feeling sexual attraction, it's not wrong if others don't enjoy the things you enjoy! Also remember that some asexual people do still have sex for any number of reasons. They may still enjoy orgasms, they may still masturbate. There is such a thing as being sex-repulsed, but it is not synonymous with asexuality.
If you have any questions, feel free to leave a comment, and I'll do my best to answer as a heterosexual and heteroromantic individual.