Its been awhile since I was in this thread!
The short answer to all your questions is that DACs, Amps, Microphones, as well as other audio-related things (like ADCs and DSPs) all are part of a quality spectrum.
I would say motherboard audio is slightly behind a flagship smartphone (LG V40, Apple iPhone 6S or 4S, Samsung, etc), and about equal to a piece of gear combining a DAC/Amp/ADC retailing for around $20-$50. Most soundcards are an upgrade over motherboard “integrated audio” (like integrated vs discrete graphics cards). To get an appreciable improvement, you would have to spend more than that, and a bigger jump in price (of well-regarded gear) will yield a bigger improvement over your motherboard... so consider your budget. Buying too cheap might leave you wanting to upgrade again soon (mfrs love that), so a short period of research and saving might get you something you’ll be more happy with in the long run.
DAC: Digital to Analog Converter. Upgrades improve detail, realism in tone.
ADC: Analog to Digital Converter. This is your mic input... similar upgrade effect as a DAC, and will make recordings from your mic sound better.
Amplifier: Upgrades tighten the control over the headphone driver’s movements, providing more “snap” to impacts and often supporting a more full-bodied sound. A poor amp might sound as loud, but weak, with a collapsed sense of distance and separation.
DSP: Digital Signal Processing. This can be EQ or noise cancelling, but for gamers this usually means Surround Processing. Better Processing is more convincing that you are “in” the middle of the game environment, or at least listening to speakers surrounding you instead of just headphones.
All these components serve to enhance each other and your final experience. I didn’t realize it till later, but my quest to improve my gaming audio and add Surround brought back quality I had enjoyed on my dad’s HiFi in my youth, letting me enjoy music instead of it just being a background mood-setting thing. If you have a Creative ZxR soundcard or something at that level, you wouldn’t hear much improvement unless you bought pieces that at least cost $100 or more each (Cavalli Liquid Spark, Schiit Modi Multibit, etc). An iFi Nano Black Label, iFi Micro Black Label, Chord Mojo, or Cavalli Liquid Carbon (and others at that level) would all trounce any mainstream soundcard on the market, but then you wouldn’t have a mic input (ADC) other than what is in your soundcard or motherboard.
Anecdotally, I found the ADC, DAC, DSP, and Amp of the Creative G5 to be quite good for the price, and I liked the idea that it (or the successor G6) could be upgraded later by using the optical output. I also liked the Sennheiser GSX1000 with the Sennheiser PXC37X, finding the DSP to be an improvement and the interface to be a nice touch, but it doesn’t have an optical output.