Asexuality is usually defined as the lack of sexual attraction, but another common definition is the lack of sexual desire. Some think that the sexual attraction and desire are the same, while others see it as different, and whether the two are related to asexuality is also disputed.
Personally I see sexual attraction and desire as different. Sexual attraction is finding someone to be a candidate for sexual intercourse, desire is wanting to have partnered sex, and libido (another concept that is also ambiguous) is wanting to experience sexual pleasure in some way. Using a food analogy, libido is hunger, sexual desire is appetite, and sexual attraction is wanting to eat that piece of cake that is on the table.
I personally define asexuality as the lack of at least one of the two, because they both result in a lack of interest in sex, which is the main concept of asexuality. Arguably, lack of interest in sex is also an accurate definition of asexuality. However, lack of libido would fall under the grey-A category, since it has less to do with sexual orientation.
Robin’s definitions are pretty good at separating the various main components of sexuality as I understand it. Even if the food analogy has all but been worn out, it still remains one of the more relatable ones out there. I would venture though, that most asexual people in fact lack both of the above, as I understand desire to be more of an extension of sexual attraction than a separate set of feelings.