If you decided to stay in school, then you did so for two more years, and then you took A-level exams, and they functioned as college entrance exams. Is that right?

University entrance exams. Calling them college entrance exams in Britain would only confuse people. In Britain "college" means (as Rob said) either a place you attend between 16 and 18 to study your A-levels (that's if you don't carry on in the same secondary school; not all secondary schools offer A-levels), or, a part of one of the few universities (Cambridge, Oxford, Dublin, Aberdeen) that are in fact collections of affiliated colleges.

Cambridge and Oxford, by the way, also have their own entrance exams (for science subjects, at least), that are taken at the same time as A-levels. Or at least, they did in my day.

The only place where I suspect I'm wrong is that the people that stayed in school from 16 to 18 took the O-levels as well.

They do, yes. Usually they won't let you stay on to do A-levels unless you got fairly decent O-levels/GCSEs, although that's a lot more flexible and informal than university entrance tends to be.

And all of these exams are separate for each subject, right?

Yep.

The only other thing I'd add to Rob's explanation, is that schooling for ages 4-11 is sometimes called "primary school" and 11-18 "secondary school".

Peter