"Net neutrality" means that service providers and other companies who are in the business of transferring internet traffic from one place to another, have a completely neutral stance on what is transferred from where and to where. They do not give special treatment to data coming from or going to specific internet domains. They just transmit data from place A to place B, and that's it. Everybody is treated equally.
Why is net neutrality important for end users? There are many reasons, but one of the most important ones is that it keeps prices down. In other words, you, as an end user, end up paying less for online services, such as for example online video rental services.
Why? Because net neutrality ensures healthy competition between companies. All companies are on equal footing when it comes to online services. Companies compete with each other with amount and quality of content, rather than the amount of lag that you experience when you access their online services. And as we all know, healthy competition in the market drives prices down: In order to succeed you need to sell your product cheaper, or else customers are simply going to go to your competitor.
Some big corporations do not like this, and thus are pushing for getting special treatment from internet service providers. In other words, they want to pay money to ISP's so that their services will be accessible at normal speed, while everything else is accessible at only a fraction of that speed.
In the end this would kill smaller competitors who can't afford to pay this "protection money". For example some smaller online video rental services may find themselves in a situation where their customers can't actually watch their videos, or the videos are of much poorer quality, because the connection is too slow.
And what happens when smaller competitors have been driven off the market? Prices will raise. That's the inevitable consequence of achieving a monopoly (or a cartel) status on the market. In other words, you will end up paying more for the same service than now.