The best definition I've seen is that asexuality is a lack of sexual attraction. Physiologically, some asexuals may still enjoy sexual stimulation, but the mental/emotional connection is not their and it is not directed at any particular person. Libido/sex drive (the desire for sexual stimulation) are separate from sexual attraction.
An asexual is someone who does not experience sexual attraction. They may experience other types of attraction though, such as platonic attraction, or romantic attraction.