Actual sepia toning of silver/gelatin prints works by replacing some or all of the silver with a substance that doesn't react as readily to oxygen (tarnish), so it made prints last longer. It also lends a warmer (browner/yellower) tone to the image, which can be very pleasing for some subjects (particularly people, where a stark black-and-white or a colder/bluer toned print is more "mechanical" and less organic).

As an effect on a digital photograph, it's entirely an aesthetic choice. It makes no difference (usually) to the longevity of the print. If it looks right, it is right. If it looks wrong, it is wrong. It's entirely subjective, but it's usually a better idea to go slightly warm (not necessarily all the way to sepia) with, say, a portrait than to go cold or to make a pure black-and-white. It just seems more "alive" to most people, but, again, that's subjective.