From your profile it looks like you run music to your headphones either from your cellphone or your PC. In both cases, the source device has digital-to-analog (DAC) circuitry as well as rudimentary headphone amplification circuitry. But as you seek more and more quality/fidelity from headphones & headphone music, you'll find that having a separate/standalone DAC and headphone amp can produce sonic improvements. This becomes especially important if you ever invest in higher cost & quality headphones.
DAC: This topic can get long, tangled, and highly subjective--everyone recommends different DACs. I'll just say 2 things here:
- Your 1st separate DAC can be a good quality DAP (digital audio player). Especially if you primarily listen to music on the go, a good quality DAP can be not just a storage place for lots of music (more than most cellphones), but also can do the DAC duties for your system, if its architecture/design allows you to take the output of its internal DAC to another device (the headphone amp).
- There are also some good quality DACs to be had for not a lot of money. Are you aware of Massdrop? Massdrop occasionally has a drop (offers to sell) a very low cost but well reviewed amp by Grace Designs, the SDAC. Here's a review: https://www.headfonia.com/review-massdrop-x-grace-design-sdac/
Headphone amps: There are many to choose from. Many are expensive, but some of the better ones are not expensive. A good example of the not terribly expensive kind is another occasional Massdrop offering, the Cavalli CTH:
https://www.massdrop.com/buy/massdrop-x-alex-cavalli-cth-tube-hybrid-amp (this is a tube/solid state hybrid). Another option is a straight solid state headphone amp also by Massdrop/Cavalli, the Liquid Carbon X;
https://www.massdrop.com/buy/massdrop-x-alex-cavalli-liquid-carbon-x-amp.
Note that I'm sending you to Massdrop just for convenience purposes. But there are dozens and dozens of potentially good/cheap DACs & headphone amps to be had. You just have to keep reading & asking questions.
Re amp designs. There are 3 types of headphone amps, similar to the amps used for speakers:
- Solid state: all the power comes from opamps and/or transistors. SS amps come in many sizes/shapes/power ratings. It's probably safe to say that most people in this hobby start out w/SS amps.
- Tube: all the power in tube amps comes from glowing tubes rather than the opamps and transistors used in solid state. Pure tube amps tend to be somewhat more expensive. Many here love the sound of tubes (I'm one of them). That's a long story, though. Tubes are the oldest/original technology used in sound production. There is something entrancing about the glow of tubes (the sound they make also sorta glows).
- Hybrid tube+solid state: there are multiple ways that the designers of these amps configure them. The most common is a tube preamp section followed by a SS power section, allowing some sonic "flavor" of tubes to be heard, but plenty of output power from the SS portion.
Both straight tube amps and hybrid amps allow the user some latitude in "tube rolling" (swapping stock tubes for aftermarket ones, new or old, chosen for sound quality). Tube rolling is a bottomless-pit type of topic, way beyond the scope of this post.
There's no right way or wrong way to any of this. If you can hear small differences in sound produced by different headphones, different DACs or amps, then you might do like others here do & "chase the ideal sound" (spending lots of $$ in the process).
Above all, it helps to love music greatly. Otherwise none of this would matter in the least.