These are probably the auxiliary brake levers found on many older road-style bikes, which sweep in so that the brakes can be actuated from the tops of the drop bars.

I hope I don't sound like a snob, but you could generally take these as an indication of a bicycle that's below "enthusiast quality." The extensions can be removed, although this will often leave a "stud" sticking out the side of the brake lever and would require a bit of brake adjustment in most cases, to take out the additional cable slack left over.

As for safety, they have less brake power than the "real" brake lever (long story made short), and your hands will be close together if you're using them, which is not good for control.

If you cannot afford a fancier bike, ask the shop if they'll sell you the bike with a different set of levers that don't have the extenstions. Another option is to remove them, readjust the brakes, cut the studs off (if present) with a hacksaw and smooth the cut with a file.