I am not familiar with that brand but I can't imagine it'll help make your headphones sound better.

first i'll answer your question: a DAC is basically a soundcard that connects (usually) via USB to your computer. They can improve sound quality over the internal DAC on your motherboard, because they are purpose-build and has way less interference than internal components do. A DAC converts a digital signal to an analoge signal.

most DACs also have an amplifier section, so they are sometimes also called a DAC/amp.

an amplifier will amplify an analoge signal. The headphone output from your pc can be too low for your headphones, and in that case you could plug an amplifier into the line out, and connect your headphones to the amplifier.

I would go with a DAC/amp in your usecase, because the dt770 don't require a lot of power, but a DAC/amp will improve the sound quality and will have more power than the onboard audio.

The reason I said I believe the amp you bought won't make it sound better is because it seems to be build for a different usecase (to split 1 signal into 4), and so you're paying for components that have no real use for you, but it'salmost too cheap for what it should do.

Although not as cheap, I would recommend you check out some of iFi, Schiit, FiiO or Topping's dac/amps. Their cheaper ones usually range between $70 and $150.