Oxford is a collegiate university (like Cambridge and Durham, although we don't like to talk about them), with each student belonging to a college or private hall. I can't remember how many colleges we have - it's a bit like trying to remember how many states there are in the US, the number seems to vary. If I tried naming them I'd probably get to about twenty-five, but I'm sure there are more than that. Essentially, the University is responsible for your education, while the college looks after your day-to-day life, although the boundaries between the two do get a little blurred. Lectures and laboratory sessions (if you're a scientist) are all organised by your department, but you have classes and tutorials (like traditional classes, but with a much higher tutor/student ratio) in college.
Every college is different, and each has its own character. The students at each college are often considered to belong to specific stereotypes - Merton students are said to work the hardest, for example - but in reality you typically find that few adhere to these stereotypes. There's a lot of variation in size as well, both in terms of numbers of students and physical expanse. Some colleges are tiny, tucked away down back alleys, while others have grand facades that lead to even grander quads (quadrangles - basically large, often grassed-over courtyards).
Your college is your home, and the members of it are your family. You form such a close-knit community when you arrive, that your real home can often quickly start to seem strange and foreign to you!