Headphones

Basically the title. I never had and amp in my life, Fidelio X3 are my first "good" phones. I wanted to know if I should buy that DAC, or other or none. Also, what am I expected to happen? Just louder music? Or some corrections (I say it and it sounds stupid because in no way it can understand what the headphones are like)? It is a portable DAC means that if using in a phone, it drains the battery a bit faster right? Same for a laptop I suppose, but if plugged in it has no impact. Also, how does it deliver the power? Is there a way to control it? Or automatic? I read about the rule of eigh, but it doesn't show anything to regulate.