Oxbridge is a portmanteau word used to describe the old English universites of Oxford and Cambridge. It is used in similar contexts to the American term Ivy League, in that both universities are world-famous and world-class, with high competition for places among applicants. Both universities are famed for their almost mystical interview process, in which an applicant may be asked to throw a brick out of a closed window, grab the attention on an interviewer who is reading a paper or extrapolate on the qualities of a banana. In reality, however, these sorts of questions are very rare, and as the interview is left entirely in the hands of the interviewer, they are becoming even rarer as older, more traditional professors retire.
The term, (with its alternative, "Camford" which is no longer used) was first recorded in W. M. Thackeray's "Pendennis" (1848-50).
Reference: "Brewer's Britain and Ireland"
See also The Russell Group