There's a few more things to take into account...
- Perceived Sound Quality: Sound Quality vs. Sound Signature
In my opinion, it's all about perception of sound quality. We are all different and have our own taste in music. Better "technical" sound quality (as in SQ by the numbers, measurements and such) isn't always perceived as better. Even the most expensive, technically perfect amp can be blown away by a cheapie china special if the sound signature of the cheapie matches your personal preferences better. Think of it as listening to music on a perfectly tuned setup in a laboratorium vs. going to a live performance. By the numbers the lab setup will sound better, but you're missing out on the ambiance and other factors of the live show that (can) add to the total experience.
- What kind of output will you be using with the amp?
If you plan on using the headphone out as the input signal for your amp, a lot of the comments are correct. There won't be any increase in SQ, it'll just go louder. Depending on the SQ of the headphone out, it could even sound worse, as an amplifier doesn't just amplify the good, but also the bad. The "crap in, crap out"-principle. Look for info on "double amping" here on the forum, you'll find plenty info. The headphone out on some players is quite good, the headphone out of a Rockboxed Sansa Clip+ at 0dB is considered 'near line out' by some folks.
conclusion: When using headphone out, SQ will not improve, Perceived SQ on the other hand, can improve.
If you are planning on using a line out from your source, the effect on the SQ can be much more dramatic. As the internal (and for many devices quite terrible) amplification is bypassed, the signal going to the amp can be of much higer quality. Line out on a portable player isn't a very common feature. Examples of players that do have it are the Nationite S:Flo 2, Fiio X3, iBasso DX50 and some of the really high end players. Other players provide line out functionality via a LOD (Line Out Dock, which isn't always an actual docking station, it can be a cable as well), examples of these are (some) iPods, (some) Sansa players, (some) Sony players.
conclusion: When using line out, SQ can improve. How much depends on the differences between the external amp and the internal amp of the player.
Another option that was already mentioned is digital out from the player, this could be coaxial (Fiio X3, iBasso DX50), optical (some older iRiver players), USB (some smartphones or tablets), proprietary (Apple does this). It could be something else, but these are most common. This can have the biggest impact on SQ, as the player will only be a transport and you can choose an external DAC and amp that match your preferences. This will allow for the most flexible setup with separate player, DAC and amp, but going this route usually ends up very expensive and you often go from portable to transportable.
conclusion: When using digital out, SQ can improve. Keep in mind that just an amp will do you no good here, you need a DAC/amp combo or separate DAC & amp.
No headphones benefit from an amp alone, there has to be a source as well. Maybe you can tell us more about your total setup, what player are you using? What connection options do you have? And ofcourse, how much do you want to spend? With that information we might be able to give you a nudge in the right direction.