In its purest form, an amplifier optimized for driving headphones. Headphone amps generally can safely handle a wider range of output impedances, so that multiple pairs of phones can be chained off of one output.
Some headphone amps support multiple, independent outputs, so that several listeners can plug in at once, and each have control over their own volume level. Some headphone amps have several input formats (analog, various digital) so that the user can switch among sources for listening. Some headphone amps also offer a “more me” or aux input, where an additional signal, such as microphone output, can be routed to just one set of phones. This allows a somewhat customizable mix for each set of headphones that are plugged in. Other features might include mono/stereo switching for each headphone out, EQ or tone controls, stereo balance controls, mute switches, and more.