If your father is described as handsome, it means he is good-looking, attractive in a classically masculine way. If your mother is also called handsome, it means while she's striking, if not exactly pretty.
Handsome is always a compliment, an admiring way of describing someone, although it's sometimes used as a way to describe a woman who's not conventionally attractive but is still interesting-looking. You can use it to describe an object as well as a person, in which case you are most likely talking about something that's really well-made, or of an obviously high quality, like a particularly handsome oak dining-room table. Occasionally, people talk about a handsome amount of money or a handsome number of votes; this is a generally admiring way of describing almost anything.