Medieval Social Order
Of course family was important. Family is always important; it always forms part of the very foundation of society. Family in the Middle Ages, however, was both more important than you might think and took on different forms than you might expect.
When we say family we most often mean those who live in the same house, excluding live-in servants (if we have any!). There are other times, though, that "family" means something wider. A family reunion, for example, entails more than one household. Someone researching family history is including an even wider circle of people. If a scholar encounters the word "family" in a document, what meaning should be taken?
So it was in the Middle Ages, but with more nuances. Famiglia in Italian, la famille in French, familie in German, "family" typically included servants and other dependents. In the narrower sense, it was only those living under the same roof. In the wider sense it could include a great many people who were dependent upon the family in one way or another. In other words, the wider sense of family included everything we would include, but more besides. Sometimes those dependants would be called "clients" (clientela), which doesn't mean client like an attorney has, but people for whom the head of the family was a patron, a man who would vouch for them and protect them and help them, in exchange for which they owed him loyalty and support. The word patron comes from the same root as the Latin for father (pater), which shows the family-like relationship.
As a historian, you must always be aware of the sense in which your source document means the term. Often that's impossible, which makes coming to grand conclusions about "the medieval family" extremely tricky.
The Nuclear Bomb
A common myth about medieval families is that they were "extended" — that is, that a medieval household consisted of multiple generations all crowded together into one house. Depending on the slant of the stereotype, this either emphasized poverty and squalor, or it emphasized nurturing and family solidarity.
That's not how it worked. Any static description of a household is a bit like a broken clock: it's right only twice a day. There were times when a given house might hold only a married couple. Later, it might be the couple with children. If they were wealthy enough, they might have one or more servants. As the children grew up and got married, they moved out, the women into the homes of their husbands, the men into their own houses. As the couple grew old, they might stay in their home or they might yield the home to one of their children and go live in a smaller place. Not unlike how things work today.
In cities, family structures could be more complex. There's more evidence of truncated families—bachelors, singles living in groups, multiple families sharing expenses. Family connections among the better sort were even more complex, with servants and apprentices and live-in nephews and neighborhood clients all in some sort of relationship with the family, and with brothers and uncles and grandfathers in their own complex of relationships. You will go far in your understanding of medieval urban politics if you understand the family dynamics involved. This is one reason (of many!) why medieval politics so often reads like soap opera.