Essentially, both Oxford and Camridge run a collegiate system, whereby undergraduates live (at least in their first year and normally in their third years too) in College, are generally taught their tutorials in College but go to lectures outside of College.
So, for example, if you did history (which I did), then most of the tutorials (weekly, one or two hourly, intense discussions on the essay you've written that week)will be taught by academic staff (tutors) who are affiliated to that College (whose studies are there, who eat there etc). Sometimes, if you choose a particular aspect of your subject that your College tutors don't know much about, then you may go to another College for tutorials in that course.
Lectures are given outside of College, where you meet all other undergraduates from all across the University. Similarly, if doing a science subject, lab classes are taught outside college. Also, all social clubs - University Societies - have members from across the universities, whereas each College may have its own clubs too (especially rowing clubs and sports clubs).
In terms of choosing which college to apply for, some only offer certain subjects (for example, the College I was at, Wadham, didn't offer geography). Some colleges have a religious slant (i.e. lots of want-to-be priests, monks etc go there and study theology). Some cater exclusively for postgraduates. Some are quite small, others have hundreds of students. Some are extremely rich and can offer amazing bursaries to their students (e.g. St John's, Christ Church) whereas others aren't particularly wealthy (St Hilda's).
It's worth doing lots of research, as you can find out the number of applicants per place at each college, and the success rate. Therefore, sometimes, you can maximise your odds of getting into a college by applying for a subject where there's a 50% chance of being offered a place, rather than a 5% chance for the same course at another college.
It's worth going along to any Open Days, either at the Colleges, or within the subject faculty. Have a look at the university websites.