The "information superhighway" analogy isn't perfect, but I think it is close enough to correct to be a useful analogy while being familiar enough for laymen to understand.
You can think of the Internet like our system of roads. There are major interstate highways; these are the backbone of the Internet, with many lanes of bandwidth. Smaller highways connect to the major interstates; these are run by your ISPs. Even smaller roads lead from those smaller highways to your home. When you send an email or type the address of a website into your browser, that message is broken into small pieces (say small enough to fit in a motorcyclist's pocket) that are carried along the roads, highways, and interstates to the destination of the email or the computer that hosts that website. If one of those small pieces gets lost, the destination computer sends a message back asking the sending computer to send another copy of that piece.
At the interchanges between the interstate and the smaller highways and the smaller highways and roads, there are stop lights, yield signs, signs describing how to get to certain destinations, and other traffic control mechanisms. As a road becomes saturated with messages on motorcycles, the "highway patrol" will tell messengers to wait their turn before proceeding onto the road, or to take a detour to another less congested road. By detouring messages to different roads, messages can still get through even if one road is busy, damaged, or blocked by censorship.
The principle of "network neutrality" or "net neutrality" is that all the motorcycle messengers on a road are treated the same. But some ISPs have noticed a lot of messengers wearing the Netflix logo on their jackets traveling their highways, and so want to restrict how many Netflix messengers travel on their highways for free at the same time. [While I use Netflix in this explanation, this could also affect other companies that send lots of messengers along the Internet.] Their plan for "fast lanes" is to set up a toll booth on their highways, and if too many Netflix messengers want to go through at once they'll have those messengers wait in line. Alternately, Netflix could pay them to set up an "EZ-Pass" lane to the highway; if Netflix is willing to pay a higher toll, the ISP will let those messengers pass through the tolls more quickly. Opponents of the "fast lane" plan worry that if an ISP has many EZ-Pass lanes for various companies, it will result in messengers whose companies DON'T have EZ-Pass (like small start-ups that can't affect the EZ-Pass) being stuck at the tolls for a long time while their competitors' messengers fly through unslowed.
Another possible solution to the problem of congestion on the Internet would be for companies to make the interstates, highways, and roads broader so they can carry more traffic. In the real world, we can't always expand roads with more lanes because of existing buildings lining them or other constraints. In the Internet, those land-availability constraints don't really apply (though there are a few other constraints.) However, one constraint that exists both for real-world roads and for Internet roads is that expanding roads with more lanes costs money.