[Matt V]

Can someone point me in the direction to how a headphone amplifier works and exactly what it does?

I am wanting an amp to get the most out of my headphones but trying to make sense of everything. I have a HTPC going directly to a home theater receiver via digital optical which goes out to my 5.1 but I'm trying to understand how I'd incorporate a headphone amplifier into that.

 

[NA Blur]

First, your home receiver has a headphone jack yes?  If so, then it uses a class D amplifier.  Most headphones amps are class A, which typically means you gain a little performance, but also lose efficiency.
 
Before you look into purchasing a headphone amp what headphones are you listening to?  What do you like and dislike about them?  There are many headphones out there that may do the trick and an amplifer may not solve your problems with your current set of cans.
 
For example:
Grado SR-80i
I like the mid range and highs and the impactful bass.
I dislike the lack of deep bass and sound stage.  The comfort could be improved upon as well.
 
Here is the wiki on headphone amps:
http://en.wikipedia.org/wiki/Headphone_amplifier
 
In short a heapphone amplifier is a device that increases the voltage from a source and delivers said voltage to your headphones.  Because headphones are analog the headphone amp will either need a DAC stage or your music will already need to be processed from digital ( CD ) to analog prior to being fed into the amp.  A headphone amp should allow good control of the current delivered to both the voice coils and driver on a given pair of headphones.