Another way publishers use this tactic is if they need to go to another printing of the comic book. Sometimes a comic book will be very popular and there won't be enough of the comic to satisfy demand. To signify that it is different from the 1st edition, a significant thing in the collecting world, different printings will often come with a new cover.
Some companies have come under fire for their use of variant covers, as many view this as just a way to exploit fans that like to have complete sets. Instead of having to buy one comic, they have to buy two or more to get all of the covers. A famous case for this was X-Men #1 by Jim Lee, which had five different covers. The comic went to sell over eight million copies.
The subject for the variant covers for lack of a better term, varies a lot. Sketch covers are popular, just showing the black and white pencil drawings of an artist. Zombie covers have become popular, showing the characters of the said comic as decomposing, brain eating, monsters. Some variants are just another colored drawing, the vision of a different artist.
Whether one agrees with variants or not, the fact is that they are still a popular thing in the collecting world. Some view them as a plague on the comic book world while others see them as a must have item to complete the collection.