Perhaps I can better explain this since some are confused.
What this supposedly would not allow is a cable company BLOCKING lawful traffic. So say, you can't have Cox Communications blocking YouTube or Comcast blocking Netflix.
However, what it appears they ARE allowed to do is say charge you an additional fee when you watch videos from YouTube or Netflix.
This is not the same as currently. The "Tiers" you look at currently are not about what kind of data, but how fast. 5 MBps, 15 MBps, 25 MBps, etc. Theoritically, you're paying for the speed and what you do with said speed is your own business.
Now, you may pay for a 5 MBps plan, and you get to go at that speed. However, if you choose to use your 5 MBps speed to go watch NetFlix you get charged an extra $.10 per "X" amount of data you're using.
Or say you really like Warcraft, but Verizon cuts a deal with Bioware to make the new Star Wars "The Old Republican" their MMO of choice? Well, you may be paying for a 5 MPbps plan, but if you're playing WOW (or any other MMO) you're getting charged extra for the data usage while you wouldn't be charged extra for playing SW:TOR.
So what it is essentially opening the way for these telecoms to do is charge you a certain price for the SPEED of your plan, but then restrict how you actually use that speed by charging you more if you use said speed for websites they don't want you to use.
To give you an analogy, lets say you rent a car that can easily go up to 80 MPH. You expect to then be able to use that car in whatever fashion you need that is normal for driving a car. However, lets say they then state that if you use the car on the open highway it has a governor on it that keeps it from going over 40 MPH. But if you use the toll road, which was paid for by the government but the car company operates, then it'll work at its full 80 MPH speed.
This is majorly aimed, initially, at things like NetFlix or Amazon On Demand, because Cable Companies can then jack up the price of their plans by offering THEIR on demand services as part of it while charging you for using other peoples.