The issue is pretty simple, actually.
Until recently, the Internet has been unregulated because the telcos hadn't done anything to really restrict the flow of information. In recent years, though, the telcos have made it clear that they want to throttle different types of traffic that either compete with other services they offer (think VOIP, video streaming sites) or are defined nebulously as "too much of a burden" (think file sharing services like BitTorrent and also video streaming sites). Some telcos are already doing this.
"Net neutrality" is an effort to keep the flow of data open and unhampered by the telcos. Once a user pays for a certain level of access to the Internet, that user should have fair and equal access to everything on the Internet, not seeing some sites or protocols throttled or shut off because they are deemed to be of a second class by the ISP.
It's only recently that we need regulations or a regulatory body to keep the ISPs in check, and that's why some groups are mischaracterizing the efforts in a negative light as "regulating the Internet" or "government control of the Internet". Like it or not, ISPs (at least in vast areas of the USA) are effectively monopolies and the rules of competition don't apply. Most people have only up to two or three choices for Internet access, and that means the telcos have all the power in the relationship, which in turn means that a third party may be needed to oversee them.
edit: But to answer your question, sadly, no, I don't know of any good, short video to explain all this to laymen.