As soon as you start with BA you get access to what are called 'Hotlines'. These are confirmed tickets that you can give to anyone, you can book these 20 times a year. This gives you approx 10% off the ticket price.
Then after 6 months you get access to the 'ID90' tickets which gives you 90% off the full fare , so for instance you can get to New York for about £140ish. These are not confirmed and you only get on if there is space on the aircraft. If there are others staff travellers on the same flight who gets on is determind by date of joining for those on the same priority.
There may be others who have a higher ticket priority than you but have a later Date of joining and they would still get on ahead of you. It can get quite complicated but I think they are simplifying it next year.
For European flights these days due to stupid amounts of tax the Hotline is often only £15-30 more than the ID90 so if you definatly want to get there then that is better to go for. Also Lowcosts and even people like Lufthansa are sometimes cheaper than BA staff travel round Europe.
Where it comes into its own is longhaul, then it is a lot lot cheaper. But there is still the tax. A New York Return costs £140, the fare there is £100 and back it is £40. Out of the UK there is £70 tax and back only £9 tax!! Ridiculous!