The "Network Neutrality" meme has been applied to many specific positions, but perhaps the least problematic is the idea that Internet Service Providers (ISPs) shouldn't treat users or content differently. It's a variation of the long-standing "common carrier" policy in telecommunication networks, and is being championed by the current FCC commissioners and the White House..
The White House is also championing another policy effort set up to protect the fights of copyright owners, called "Copyright Alerts." Copyright Alerts is a partnership of the larger ISPs and movie and music industry groups to "fight online illegal downloading of copyrighted works." The new enforcement system enlists the ISPs to help monitor subscribers' Internet use, sending notifications of suspected illegal downloading, and administering penalties that include slowing down or even denying user access to the Internet through their ISP.
So in this case, the White House is asking ISPs to not be "network neutral," but to discriminate against certain users based on the presumption that they seek certain types of content. And since this action can also be looked at as a "conspiracy in restraint of trade" - collaboration and collusion among competing firms - it's likely that the plan has been vetted by both the Dept of Justice and the FCC, groups who are supposed to be concerned about anti-trust behavior like this.
And while I'm not a lawyer and am basing this on several news counts, it seems that this is also a considerable expansion of copyright law by private fiat. Current copyright law puts the onus of enforcement on the copyright owner, who must work through the courts to seek redress. In this case, it looks like the copyright industry is enlisting the aid of the ISPs to not only monitor for illegal activity, but for the whole enforcement process - the ISP becomes the investigator, the plaintiff, the judge, the jury, and the enforcer of "alleged" copyright abuse, all without the courts or any degree of due process.
The next time the FCC or the White House talks about Network Neutrality, remember the asterisk that now goes with that support. Network Neutrality means no discrimination*, *except when it benefits your cronies and supporters.
Sources: "Top ISPs become copyright cops", cnet News
"Exclusive: Top ISPs poised to adopt graduated response to piracy", cnet News