Fantasizing about someone means that in a direct, or indirect way, someone has left an imprint on you mentally, physically, or emotionally. As a result, you are now creating imaginary scenarios involving them.
Fantasizing is similar to day dreaming. A person who is very interested in old cars, for example, may daydream, or fantasize about owning a vintage car, or driving one down the road. Fantasizing specifically about another person does not mean that you are sexually attracted to them. All fantasies involving other people are not sexual, and some may be completely platonic. One may fantasize about belonging to another family, or having a parent different than one's own. However, sexual fantasies are quite common. Fantasy is closely related to experience and desire. Having an emotional, mental or physical desire for something may also cause you to fantasize, or imagine experiencing that thing in specific ways.