There are two technical reasons for amps.
First goes on the premise that the headphone jack on your source device has an built in headphone amp, but the quality of the amp is an afterthought. It might use the cheapest quality circuit design and parts to give you sound through your headphone jack. So an external headphone amp connects to your line out jacks (unamped/unprocessed signal), and replaces the built-in one. Instant better sound as you outputting a passing cleaner, less distortion ridden signal. The headphone amp circuot is better designed to provide all the pitch (frequencies), and be quick (it can response to changes in the music). There are other characteristics, but overall, you'll perceive the sound as beening clearer, punchier, more detailed, crisper sounding, smoother etc. Different amps have very slight sound characteristics...some can sound smoother, some can sound punchier. When you have experience, you can start picking out fine differences.
The second need for an amp goes on the premise that some headphones are hard to power. Think of a small engine in a big car. It works, but it struggles. With some headphones, their impedance, a measurement of its electrical load, gives some built-in headphone jacks too much work, and it can't do a good job. If called on to produce a difficult signal, the amp can't put out enough power, nor respond to the instant and varying demands of the music. A good headphone amp will handle it with ease, without strain, to handle all sorts of headphones, even high impedance ones that tend to be too much work for the typical portable.
Hissing is just caused by a circuit design that isn't completely quiet when presented with certain loads like low impedance headphones. It's not the end of the world, but can be a bit annoying if you listen to music with a lot of quiet breaks.
