I'm on Eurofleet/LHR and having come from an airline where bidding didn't exist, it's a nice touch.
As someone has already mentioned, it's an imperfect system in the sense that you won't always get what you ask for, but there are ways of improving your chances.
The system basically allows you to bid for your days off, or for specific flights or nightstops in specific locations. You get a points system that runs from 1 -200 whereby the more points you attach to a specific request, the more you want that specific request.
For instance, bidding 200 points "all nightstops" basically tells the computer you're desperate for loads of nightstops, but you don't really care where they are.
You might then put a second bid in, 150 points for an IST nightstop. The computer will then try to find you 1) A few nightstops, anywhere 2) In addition, a nightstop in Istanbul.
You can also bid for your days off, rather than have them randomly allocated by rostering.
However, the more bids/requests you make, the more difficult you make it for the computer to decide what to give you, as at BA, there are 13,000+ other crews' requests to deal with.
My advice, keep it VERY simple. When making more than one request, space out the points you give to each request by at least 50 - make it easy for the computer to see what you really want, and what you're not really bothered about.
Everyone has their own way of bidding, and different success rates, but the above is a good start.
It's a nice perk, but you won't be able to write your own roster with it! Most crew at BA appear to be quite happy with it.