Your counsellor is right. You pick one which is your first choice, your Firm as UCAS call it, and then another, usually with a lower offer, which is your Insurance. Your other two offers will thus be rejected.
eg. Firm: University of Edinburgh, Medicine, Conditional offer AAA
Insurance: University of Bristol, Biomedical science, Conditional offer AAB
The above candidate (who is totally fictitious, I don't even know the offer for either course) would by doing this reject an offer of University of Leeds, Medicine conditional upon AAA.
Just seen you're still waiting upon one (Warwick, Durham or Bristol per chance who are known for that?) and in such cases I think UCAS won't make you choose until you have a decision from all your unis. Check the website though.
Sorry this was a shoddy post, realised I didn't explain the purpose of your Insurance. It's their to ensure that you are more likely to have a guaranteed, contractually binding, place at university (here Bristol) in the event you should miss your first choice offer but make theirs (here get AAB). Obviously this creates security for students and also helps to prevent absolute mayhem on British results day as the vast majority of candidates have a place confirmed one way or the other.