Lucky for you, I work in the telecommunications industry and have studied this issue for a long time (~2.5 years). Here's how net neutrality came to be, and what the ruling means now.
Back in the "olden days" of pre-internet ubiquity, fixed line telecom providers (think old, old AT&T, Quest Communications (now CenturyLink), etc.) were regulated entities that were regulated monopolies. That means the government got to decide what price things were (price controls), and had regulatory requirements for services (union contracts, bids, guaranteed service access and speeds, equipment stuff like that.) good for access, bad for innovation.
Realizing the telephony markets could become much more innovative as the internet became a popular phenomenon, the Federal Communications Commission (FCC) deregulated the telephony markets, but retained certain rules for how business was to be run in certain instances. Won't get into these now, but they come into play later. In the US, this occurred as the break up of "Ma Bell," or AT&T.
Around the same time, cable (video and internet) was becoming more popular as people began to realize data and HD video could be transported over copper and now fiber-optic wire (hence the word, cable). The FCC, back in 1996 and with the help of the D.C. 9th circuit court precedent, decided NOT to regulate broadband providers and wireless providers in the same way they regulate FIXED (aka old school telephony) providers, with fear that (among other things, such as jurisdiction) over-regulation would stifle the growth engine cable was in the economy back then. Nonetheless, the FCC determined that it had the jurisdiction to establish 3 rules for common carriers (old school telephone providers) and broadband providers (cable, wireless and satellite providers):
1. Transparency: fixed and mobile providers need to disclose network management practices
2. a no-blocking rule: fixed providers can't block lawful content, apps, services, and non-harmful devices
3. a no discrimination rule: no unreasonable discrimination of lawful network traffic.
This ruling by the appellate court in the case of Verizon vs. the FCC (which can either be remanded back to the 9th circuit or appealed to the Supreme Court (!)) essentially states that:
1. Broadband providers (which is basically all ISP's today) have the right to determine which content it is free to block (making the no-blocking rule an overreach of the FCC's authority), and
2. the no-discrimination rule is an unreasonable restriction on the broadband provider's ability to monetize their network and overreaches the FCC's authority.
The reason the court ruled in this manner is because of the two classes of regulation. Type 1 "common carriers" (such as Centurylink / old school AT&T) fall under a broad scope of FCC regulation and can be regulated as such (due to the legacy of the monopoly). But the legacy ruling by the courts and the FCC for broadband providers as Type 2 "information providers (i.e., NOT common carriers)" actually limits their authority to regulate ISP's, as they were not classified as "common carriers"; this was a fairly libertarian approach to regulation, and led to the US developing one of the strongest video content and copper / fiber optic networks in the world, at the time (early 2000's)
Considering the above information, here's what it means:
Carriers like Verizon, TWC, Charter, et. Al., have the right to block certain content. This includes Youtube, Netflix, Hulu, and NS. It also means they can slow down, or ask you to pay more for increased speeds (not necessarily more than you pay today, but you can pay for increased speeds on NS or Facebook, specifically. This happens globally already, particularly for facebook in developing countries (shocking, isn't it! great business idea actually. Some of people's first internet experiences are directly through Facebook. They mostly think Facebook IS the internet. incredible). Net Neutrality is a mostly American phenomenon: net neutrality does not exist in places like Europe or Africa, though some countries have varying interpretations (generalizing here)
So why is this a big deal? proponents for net neutrality argue that smaller websites and content creators (such as NS) will be marginalized by slower speeds and will slow down the pace of internet innovation (such as formerly nascent apps like Snapchat). Moreover, it could be argued (though I disagree) that this is anti-competitive for internet oriented companies, such as Amazon (for their shows), Netflix, Youtube, etc because it gives traditional content creators and distributors (like NBC or ESPN) an unfair advantage (FYI, Netflix is eating everyone's lunch, this argument really isn't valid). Opponents of net neutrality argue (and rightly so, in my opinion) that it cost multiple billions of dollars to build out their network and they should be allowed to charge a toll on those who are using their network for their own financial benefit, with no dividend paid to the ISP. That toll isn't on consuners; its on content creators, who are increasing their annual costs at 10% a year, and is the driving reason for your expensive cable bill. Considering Netflix is 18% of ALL internet traffic globally, this could be seen as a valid argument.
It remains to be seen what will happen next, but I think fears are overblown about this, for the following reasons:
1. Comcast, in its deal to buy NBC (huge content creators) agreed to abide by the 3 rules listed above until 2018. So if you want net neutral, Comcast is the way to go.
2. ISP's will shirk away subscribers if they block or slow down certain types of content, NS, Facebook and Netflix included. They're interested in making money, and a competitive market demands that people will switch to the provider that is the most consumer friendly. It's in their best interest to behave in a manner the consumers (that's you!) make them.
3. The way I see this working out is in the following: a personalized network. Do you want to have prioritized data traffic for Netflix on Sunday nights for guaranteed quality (high bandwidth demand time), or want to have your phone get guaranteed access to a wireless network at a football game / concert so you can live tweet it or Instagram it? That's not that far off. You might pay more for that service (or, companies will sponsor that data for you, which is more likely), but you are personalizing your network to your needs. Potential upside for the consumer there. In a net neutral USA, that cannot occur. You cannot pay for priority access... think of it like an airport security line. Some have speed passes, which they pay for.
4. Europe / the rest of the world has not seen a gigantic degradation in internet blockage; in fact, some of the worse things about the internet (child porn, for example) is getting blocked more frequently in less net neutral countries (such as Israel). Then again, that might be violating the implied libertarian-esque ideals of the internet, which have generally been very helpful to the proliferation of human rights around the world.
It's a complex issue that people tend to jump to conclusions about, but that's basically what's up and how things might shake out. Something to watch for sure: both sides of the fence are heavily lobbying to make sure their side wins. This is big guy vs. big guy.
Hope that helps!