Headphone amps are generally used by people who don't have a headphone jack on their receiver--usually because they don't have a receiver!
They are also used by people that have managed to convince themselves that there is something magic in a separate headphone amplifier that simply can't be obtained any other way. I think they're wrong, but that's just my opinion.
Another reason to use a headphone amp is when you want to you full sized headphones to listen to music from a computer sound card. Here in the office I use a Headroom TotalAirHead to drive a pair of AKG K501's from my IBM laptop. The line out, while sufficiant for my old Sony earbuds, just couldn't drive the K501's without having to fully max out the volume. With the TAH, all is much better, I can listen to my music without annoying my coworkers and with the line out volume low enough to avoid introducing any more noise than I have to.
It's not for critical listening or anything, but it is far better than it was before I bought the TAH.