I have just bought a flat and there is a notice on the board in the common areas that for fire escape purposes, the block has a stay put policy. I have no idea what that means;
There is a complicated technical answer to this question but let me try and put it in ordinary English language. In round terms, if your block of flats is built with concrete floors and a concrete staircase with a proper fire-proof entry door into your flat, and if a fire started somewhere else in the block, it is assumed that you would probably be safest if you stayed inside your flat until the fire services arrive and wait for them to get you safely out of the building. In other words: stay put.
On the other hand, if you live in a Victorian conversion with wooden floors and a wooden staircase, and a fire starts somewhere else in the building, then it is probably safest for you to get out of the building as quickly and as safely as you can. In other words: do not wait for the fire services, get out, and get out as quickly and as safely as you can.
Actually, whoever put up the notice in your entrance hall has a responsibility to make sure that you understand what the policy for your building is and there ought to be a more complete explanation, either pinned on the notice board or sent to all residents occasionally so that they do have a good understanding of what to do when they become aware of a fire somewhere in the building.