Family has meant many different things throughout history and to different people around the world. Our word 'family' comes from the Latin word familia, which often had a specific legal meaning and could mean all the people that a paterfamilias (male head of household) had under his roof or belonging to him - literally belonging, as it included servants and slaves as well as relatives. The Latin word for servant is famulus, so the connection is clear.
We tend to think of family as being husband, wife, children and perhaps blood relatives like uncles, grandparents etc. In some cultures extended family is the norm - ie, you live with, or are close to, a large network of cousins, aunts, in laws etc - in others it is the nuclear family (basically a couple and their children). In many modern cultures it is quite usual for a family to consist of just one parent and a child or children.

The family is a complex subject with a long history; you can find an initial overview here.