Here's the baggage guide on the BA website: http://www.britishairways.com/travel/bagchk/public/en_gb
For most destinations, you can take two bags weighing up to 32kg each. However, this can vary depending on where you are flying from and flying to, so you definitely need to take a good look around the website.
Different rules apply for oddly shaped and bulky baggage like sports equipement and musical instruments, so you'll need to check that out too if you're planning on doing either. The link above should have all the information that you need.