Net Neutrality is a political Internet structuring idea that requires Internet service providers to handle all bandwidth equally. Internet service would be a dumb pipe, like your water main. (Not quite like the telephone. Your telephone company knows what numbers you've been calling and how long you've talked. They are, however, prohibited from listening in. That's typically done by the government, with a court order.)
The ISPs generally dislike this, as they want to promote some traffic over others. They'd rather favor email and WWW over, say, Bittorrent. They complain that Bittorrent sucks up all their bandwidth, costing them money. (When the bandwidth runs out, you need to buy more capacity, or it'll slow down for everyone and your customers complain.)
Internet companies, like this blog's host, Google, fear that a lack of Net Neutrality will mean that they will be extorted by every ISP in the land. That every month a representative will come by and demand money, and if not granted it, will throttle all traffic to unacceptably slow speeds without quite cutting it off (because cutting it off entirely will be seen by the customer as censorship of the company, while slow access will suggest problems on their end.)
The ultimate in neutrality would be my earlier proposed grid Internet in which there is a massive array of underground routing boxes, all connected to their immediate neighbors. One could, for very little money, have a choice of connecting to one of four boxes, and connecting to several would make your own connection more robust. When connected to several, your connection would go through whichever was most available and least congested. ISPs would pretty much be obsolete. The main reason that this plan isn't being done is that it would require many many ditches dug, and land-management authority that only the government has. Also, the need for more and more routers would quickly rack up a budget in the high millions nationally. (I think connecting the entire world this way would cost in the trillions). The main advantage to it is a communication infrastructure that is for all intents and purposes indestructible.
Main arguments for opposing neutrality are to point to the Pareto principle, an economic principle that points out that many things are divided 80/20 instead of the 50/50 one would normally expect. 80% of the money is earned by the top 20 richest people. 80% of the sales are made by the top 20% of salespeople. 80% of the spending is done by 20% of the people. And so too, with bandwidth, which costs money, 80% of it is used by the top 20%. Since ISPs price their services per account rather than per gigabyte of traffic, ISPs would like to throttle down those top 20%. Or, alternatively, they could price by usage, but that doesn't sell very well.