The Good
There's lot of misinformation floating around about this so I'll go over some of the points. The basic principal of Net Neutrality is that a company like a ISP is not going to discriminate or prioritize the traffic across it's networks. This for the most part is the status quo and has been, the government is acting now because recently some ISP's have shown interest in prioritizing traffic. One example is interfering with P2P traffic, granted this is mostly illegitimate traffic and is burdensome to the ISP but that's for another topic.
Why it's important that traffic remains neutral is many ISP's hold monopolies in many of the areas they serve. What the ISP's would like to do is offer tiered services (note that there is two types of tiering and I'll explain the second shortly). As it stands now you can connect to this site just as fast as you can connect to any other site. If we take Coalcast for example that would require some significant bandwidth overall if a lot of people connected the only limit is how much my server can handle which I'm paying for. The tiers the ISP's would not be on the users end necessarily but on the content providers end which could prevent you from getting access to content on many sites like this one.
Let's say the ISP launches their own service to compete with the service I provide. What they would do is throttle the bandwidth to my site and other lower tiered sites which could squeeze me out of the picture. If you the user come to my site and it takes forever to download or you simply don't have the bandwidth available and there is an alternative that loads instantly which service are you going to choose?
Small potato sites and many of the other smaller nooks and crannies that really make the internet what it is could disappear as the ISP's leverage their control of the bandwidth to take market share. Other third party services that are not peering with them like VOIP, Video, Audio, YouTube...etc or anything that requires a lot of bandwidth could be squeezed out. Another thing they wish to do is charge the content provider for more bandwidth. A large company like CNN, Disney or whoever may be easily able to afford such costs and would probably invite it as they will then be able to also leverage the increased bandwidth to squeeze out the competition.
If you want to see a similar example of what the internet might look like if the ISPs were allowed to do this you only have to go as far as your television set if you have cable, expensive and limited choices. The internet has flourished for almost 2 decades under Net Neutrality as have the ISP's and that is why it is important the basic principals of Net Neutrality continue.
The Bad
The ISP's argument is that they will lose control of their networks and to some degree they have a point. If you have someone using P2P software and it's running 24/7 is their a reason why we should all be paying for it? Certainly not and that's why it's also important the ISP's are allowed to offer tiered but neutral services to their customers.
As long as the cap is imposed on the customer and not the content or services the ISP's can maintain control of their network and content providers will remain on a level playing field. They do have to be compensated which leads to the downside which is services may cost more as they will not be able to rely on revenue generated by their own services since there will be a lot of competition. This could be a good thing or bad thing depending on you perspective. Additionally lower income people may not be able to afford the costs of higher bandwidth plans but like with everything else... too damn bad.
The Ugly
I've seen many equating this to the "Fairness Doctrine" which to this point I have not seen anything resembling that. One thing I will say if any legislation comes to light that even remotely resembles the "Fairness Doctrine" it has to be stamped out immediately. It could certainly carry over to that.