Say you underexpose by a stop and don't notice; you'll lose some shadow detail. If you do notice, you can correct by pushing (extending development) and get back a decent image. It will have a little more contrast if you push but you can just print it with a lower-grade filter in the enlarger. You really only get underexposure latitude by pushing, so it's not so much latitude as a deliberate decision to use the film in a different way. Don't underexpose if you can help it; the more light the better with negatives.
You can overexpose most B&W films by at least three stops (i.e. 8x too long!) without causing any problem except additional grain. The negatives will be very dense but that just means they need to spend a little longer in the enlarger. That over-exposure latitude is what most people are referring to and it means you can select a conservative exposure setting and basically ignore the light levels until they change dramatically. If suddenly you end up with 2 stops more light, the image will still be completely fine for most purposes except the most exacting.
Slide film with a 2 stop over- or under-exposure will come out nearly clear or nearly black; it'll be useless in comparison to what you can do with a B&W shot.
Modern C-41 (colour neg) has as much overexposure latitude as B&W but it's more difficult to recover from because the saturation generally reduces with overexposure and some colours can go wonky, which is hard to correct for using only analogue techniques.