In NYC, a .5 bedroom means that there's a room that can function as a bedroom but that does not fit the legal requirements for a bedroom. Sometimes they're listed as 2 bedrooms plus an office, too, although that usually means the extra room is tiny.
In our case, the condo is currently a 2 bedroom, but one of the bedrooms is huge (for NYC; 30 feet long by 12 wide), so we are putting up a wall to split it roughly in half. But one of the new rooms will most likely not technically be a bedroom under the law because it doesn't have a window overlooking a sidewalk or courtyard, just to an air shaft (it's a fire code thing; essentially, the new bedroom will not be easily reachable by fire fighters from the exterior). This only matters if we were to rent the 'half' bedroom or if we were to sell it. The law restricts how it's sold or rented, not on how owners use it for themselves (although the city could deny the work permit to put up a permanent wall; if they do, NYC has a big market for 'temporary' walls indistinguishable from real walls that do not require permits).
When we sell it many years hence, we will not be able to list it as a 3-bedroom, but as a 2.5 bedroom. Since the new room will be plenty big to use as a real bedroom or nursery, we wouldn't call it an office (though that is how we'll be using it until we have kids). The condo also couldn't be sold for as much as a similar unit with three bedrooms. But I'm not worried at all about the unit holding its value for decades.
There's nothing like buying a new place then waiting two months to move while work is being done. :/