The basic idea is that the internet should carry all traffic equally, no one's data gets preferential treatment.
This is already been forfeit; services such as VOIP phone traffic don't work unless given preferential treatment. Through QOS info in the data packet's headers, VOIP traffic is given a higher priority than your traffic from Netflix, for example. If they really wanted true neutrality, QOS wouldn't even exist. All traffic gets the same priority, and if your gadget can't work with that, fine, your gadget can't work. But too many people like their internet based phones, so this practice has already been accepted.
The current debate is whether or not traffic carriers and ISP's should be able to charge customers a premium price and in return, give that customer's data a "fast lane" in comparison to "ordinary" traffic. Netflix for example, could pay it's carrier the premium, and any traffic coming to or from Netflix would be carried at a faster speed than Joe's internet TV company, who is just starting out and can't afford to pay the premium.
So, on the surface, NN sounds like a good idea. Except that is already impossible to achieve.
I would strongly favor legislation requiring true neutrality; all traffic has to be handled identically. But that will never happen. QOS for VOIP has ensured that outcome.
The real fear, at least for me, is that current efforts to legislate what they are calling NN is really just another in a long line of attempts to establish precedent for government control and eventually censorship of the Internet.