La familia extensa simply means extended family. There is a term in English as well, which denotes more or less the same thing. It refers not only to your closest family (parents and siblings), but rather to the rest of your family as well: your aunts, uncles, grandmas and grandpas, cousins, everyone you are related by blood, but aren't as close to you as your nuclear family is. Sometimes, some of these people will live with you and your family in the same house, which is quite normal in many Hispanic countries.
