Wizards are magic users born with the ability to learn other people's spells after they awaken. The same term is used irrespective of gender.
They may or may not also have spells of their own. There is a rare type of wizard who do not get spells in the first place. (Almost certainly called Seer)
The process of learning spell is really simple: they just have to see it (possibly multiple times), but don't need to make any extra effort. It may be possible to learn some spell without trying for them.
Being wizard, similarly as (born) magic affinities, is caused by having the right ancestors. While it wasn't confirmed being caused by genes, it either is or it behaves similarly.
When both parents are wizards, kids should be wizards as well.