21% of undergraduate applicants, across all courses, got in last application cycle I believe (which is typical). So roughly 1 in 5 applicants get a place - some courses are more competitive than others though (for example, maths, CS, architecture, and philosophy are all more competitive than the average, with architecture being the most competitive course followed by CS). Of course those numbers don't necessarily tell you that much, as there will be an element of self selection (people who don't get top grades will probably not consider Cambridge), and not all courses are offered by Cambridge (it has no dental school, for example). Additionally applicants can only apply to one of Oxford or Cambridge - if anyone could apply to both, it would probably be more competitive due to double-dipping applicants.
If you want to apply (successfully) to Cambridge, you need to understand what they look for in applications. To begin with, they don't really care much about GCSEs - they'll be cosidered "holistically" with the rest of your application, but other areas will be more important (e.g. any pre-interview assessments, the interview, academic reference) and all the official college reps on here have stated that they have never rejected an applicant solely on the basis of GCSE grades. They also don't care about extracurricular activities unrelated to your speciifc academic area. If you are applying to maths, they don't care if you have grade 8 piano, were captain of ten sports teams, etc - those activities don't tell them anything about your mathematical ability. They only care about so-called "supercurriculars", namely extracurricular activities specifically related to the subject area you're applying to (for the maths example, things like the senior maths challenge).
Most applicants are invited to interview (I think an average of about 70-80% of applicants, varying by course); I believe Cambridge's policy is to interview anyone they deem might on paper be able to get an offer, i.e. meeting any subject requirements, being predicted (or having achieved) grades at the standard offer level (A*A*A for STEM courses other than PBS, and economics, A*AA for everything else), and meeting any expectations in terms of pre-interview assessments (i.e. having taken it and there not being any indication from that they would struggle with the course potentially).
The interview will probably be the deciding factor in whether someone gets an offer, as it is the only way they can see how an applicant would fare in the tutorial environment; the interviews are in theory at least supposed to mimic the tutorial system which is a core (sometimes primary) method of learning in a degree there. Some students don't learn as well in that format - it doesn't mean they aren't intelligent or are bad at their subject, it just means they might benefit more from a more typical lecture format at another university. The interview helps admissions tutors assess this.
Mature applicants are also looked at a bit differently; usually if you have been out of education for more than 3 years after leaving school, they will want to see some more recent academic work being done. They will look more at that recent academic performance compared to past academic performance, since the more recent work will be more indicative of your current ability. Most colleges I think indicate they don't prejudice applications from mature students on the basis of weaker academic performance in the (more distant) past. An upward trajectory in grades is also usually viewed favourably - if you did more averagely in GCSEs, but have very good A-level predicted grades and a strong academic reference, that is usually viewed positively.