Just to be pedantic, the correct spelling is Sgian Dubh (Gaelic for Black Knife).

One source claims it is so-called simply because it usually has a black handle, but the more generally accepted explanation is that it got its name because it was carried in a dark (concealed) place, and the custom of wearing it in the sock came about because it was considered bad manners to have a concealed weapon when amongst friends, so the knife was brought out of concealment and, for convenience, stuck in the sock.

Here in the UK it has no other purpose than simply decorative and is not normally worn other than on formal occasions. The blade is long enough to fall foul of the (anti) knife laws and would certainly not be allowed on an aeroplane. However, at least here in Scotland it is permitted as part of the outfit when formally dressed, in the same way as Sikhs are allowed to carry their ceremonial daggers.