TRS is a standard audio jack. you can find a 3.5mm headphone jack in your phone and that's TRS, the second most common is 1/4".
TRS stands for Tip, Ring, Sleeve (the three gold parts of the headphone cable) named accordingly from the tip of the cable to the base. The tip supports audio for the left ear (L), the ring supports audio for the right ear (R), and the sleeve is a grounding pin (GND). some old headphones only have TS, signal and ground.
Having a signal audio signal is considered "unbalanced" because the signal can be wavered by outside objects when it passes through the cable.
A balanced signal is when you have two images for every audio signal, regular and inverted (correctly labeled as hot and cold). the two signals eliminate any unwanted external signals which can affect the music. It does this by comparing the positive and negative music signals and eliminating differences.
A TRS cable can support a balanced "mono" signal or unbalanced "stereo" signal. Mono means there's only one music signal so the same music comes out of both ears. With stereo a different signal comes out of each ear (stereo is best heard in Queen's "Bohemian Rhapsody").
A TRRS has two "rings" meaning it has 4 poles (a pole is a connection on any plug or jack, TRS has 3 and USB has 4 etc.). with the 4 poles the TRRS is able to support a "Balanced Stereo Image", free of unwanted signal loss or distortion.
Obviously you know what "Headphones" are.
A "Jack" is a connection between two audio devices, hence the 3.5mm connection is commonly referred to as a "Headphone Jack".
An Amp is short for an "Amplifier", I'm confident you already knew that.
Every musical signal you hear from speakers or headphones goes through an Amp first. Amps most basic purposes are to make the music louder but with audiophiles they sometimes serve a different purpose.
Every device, even your phone has an amplifier in it to power speakers or headphones (an amp usually comes after a DAC but that's a different story, I can educate you if requested). In many cases, high end headphones have high "Impedance" making them hard to drive, again, I can tell you all about impedance as well. when you have a cheap or underpowered amp powering hard-to-power headphones, it puts strain on the amp or can lead to the unfortunate event of "Clipping", both of these harm the sound quality.
By buying high quality Amplifiers that power high-impedance headphones without breaking a sweat, the music flows freely and easily, making it sound much better. Sometimes people even buy special amps that can power incredibly easy-to-power headphones with ease, such as earphones. That's why in portable setups, audiophiles will attach amps to their DAP even when the DAP already has an integrated Amp.
I hope this could help.
If you have any further questions, just ask.
-Nemo
