What exactly is a Baccalaureate? We don't have that in Canada. Is an equivalent to a B.A.

That’s exactly what it is. Baccalaureate is just the Latin word for it.

We have B.A’s and B.S’s.

In the UK there is an alternative to A-levels being offered now, called the International Baccalaureate. Instead of choosing 3 or 4 subjects to study aged 16–18, the IB still tries to cover all the subjects, rather like their schooling up until that point. I believe the IB is common in Europe which is one of the reasons it’s started to be offered over here (some forward thinking schools offered it 15 odd years ago, but it’s only just now starting to really take off).

The IB is not the same as a BA in the UK (even though the word is Latin for Bachelor) as it is the equivalent of A levels, the qualifications required to get into university, to then study for 3 or 4 years to obtain a BA or a BSc (or BMus in my case).