Speaking from her side of the equation, because my family is important to me, basically what is means is this:
Family is the group of people who will love you no matter how many times you disagree or fight, whether they approve of your decisions or not, and who always want the best for you even if it's not what they'd want for themselves. Family is always happy you stopped by, even if they can't admit it because they're still mad at you. Some people are lucky enough that they are born into a group of people like that; others are born into a group of people who simply share genetic traits. You can't do much about your relatives, because on that score you didn't get much of a choice in the first place, but everyone builds their own family. Yours may consist more of your friends, bandmates, roommates, or old coworkers, but sometimes you luck out because they were already your sibling or your cousin or your granddad and you didn't have to look as hard for them. Age doesn't matter for family, and neither does sex.
Your family is like the highest tier of your monkey sphere, the group of people you prioritize the highest. For my boyfriend, that means giving his half-brother his paycheck when the latter lost his job, even though we are almost as broke and didn't have any money at all for the rest of that month and had to borrow from our parents just to eat. For me, it means going to like 5 holiday get-togethers a year where my cousins and aunts and uncles and grandparents and I eat a shitload of homemade food made from old recipes, tag-team handing out 5,000 pieces of halloween candy, exchange gag gifts, drink a lot of beer, and play charades and Blokus and stuff.
It also means doing stupid shit like going to your best friend's son's first birthday party, because you know the kid isn't going to remember anything and it's just going to be cake frosting everywhere after a minute, but they want you to be there, and so you go. It means learning to smile and grit your teeth while your significant other rambles on and on and on literally for hours about shit you care absolutely nothing about, because it's important to them and you just want them to be happy because they enjoy that thing. They are the people you worry about letting down (I mean for real, not the stupid shit you worry about with anxiety problems), and the people you want to keep happy, and the people you grieve with when they are sad.
You also already knew what it means. Most people do, they just haven't heard it phrased in the right words. "Family" might have come to have a very twisted meaning in your mind because of what life has thrown at you, and that's ok, as long as the underlying concept is still there. That thing about keeping your mom at arm's length? It may not be the healthiest way to go about caring about her feelings, but you do care. If she wasn't part of your family, you wouldn't make such an effort.
Camille is part of your family, too, and because this is important to her, you cared enough to ask, so keep that in mind. You're not at such a loss as you think.