Apparently somebody hasn't played WoW to see where the stole the "elite" designation from!
In WoW, an "elite" monster does about as much damage and has comparable abilities to any other creature of the same level; however, it has maybe 4 times as many hit points, so it takes longer to kill. This is more fun than just fighting a higher-level normal bad guy because the higher-level mob will kill you in a couple hits and it'll resist or deflect most of your attacks, so it's a matter of luck whether you can even connect. Generally speaking, in WoW "elites" are designed to be taken down by groups, whereas non-elites can be taken down solo.
In D&D terms, the difference between, say, a level 14 mob and a level 10 elite mob is that the level 14 will do more damage, have higher defenses/AC, and have a higher attack bonus, whereas the level 10 elite will have a bunch more hit points. The elite is a lot more fun for a level 10 party to fight, because they don't have to pray for a 17 or higher on their attack rolls to successfully do anything to the mob, and in turn their own AC and defenses will actually be helpful.