That's a good question. Net Neutrality is not about whether an ISP can charge you more for using more bandwidth. It's about whether an ISP can charge your more (or restrict your usage) based on which websites you communicate with.
One way to think of it is that we already have "electric neutrality" (not a real term), which is to say, you pay for the amount of electricity you use, but you're free to plug in any appliance you want. Losing "electric neutrality" would mean that, for example, your utility could charge you more or less for plugging in an Apple microwave than a Microsoft microwave. That would be insane. Can you imagine trying to start a company selling a new appliance if you had to pay a special fee to an electric company to stop them preventing your customers from plugging it in?
Net neutrality supporters want the internet to be treated like a utility. We are willing to pay for the amount of data we use, but we are not willing to let an ISP decide which websites should have their data made cheaper or more expensive.
An internet with net neutrality is one where you pay for access to the whole internet (perhaps per Gb or perhaps your ISP chooses to sell you a plan with unlimited data). An internet without net neutrality is one where you might pay $X for a connection that only talks to Facebook, and connecting to Gmail costs $Y more. A brand-new startup in a world without net neutrality is at a huge disadvantage if they aren't included in the package of websites that a customer buys. That's the end of the internet as we know it.