Hm... explaining it somewhat basically...
So internet speed is a thing, and is determined by the type of service you have. Currently the ones who primarily provide the internet are telecommunications companies, though there are other companies setting up their own services.
What Net Neutrality means is that the providers of the internet can't slow down the internet for specific websites (say, if AT&T wanted to slow down access to Comcast's website), or speed it up for specific websites, either (say if Netflix paid Comcast to speed up their website for anyone using that provider).
This is a good thing, because it means that there's fair competition between websites, which ensures that we, who use the internet, aren't even really aware that such competition is even taking place except as internet usage becomes easier and sleeker (or more difficult and cumbersome, depending on who you ask, but that's an entirely different topic.)
It also ensures that people who are stuck with any given provider, for whatever reason, aren't unfairly cut off from specific websites because that provider was paid to slow them down.
Now, while I haven't followed the more recent aspects of the current battles, when I last looked, the ones who were primarily against Net Neutrality were those providers, and the only logical reason I can think of is that Net Neutrality doesn't provide for any of them the maximum potential profits, since websites can't pay them to be faster.
Actually, it's the exact opposite. It's the government (specifically the FCC) trying to make sure things stay more or less as they have been, so the megacorporations don't screw it up for everybody.