Net neutrality isn't sexy, but like basic services you rely on daily, such as water, gas and electricity, you are going to care deeply if it gets interfered with. For an entertaining overview of the problem, John Oliver has you covered:
The essence of net neutrality is that all data flowing through the Internet is treated equally. (For newbies, "data" could be anything - searches, web pages, videos, Facebook, cat videos, emails, Skype calls, and so on). The net being neutral means that whatever you are doing online, and with whosever services you choose to do it with, you will be able to do that when you want, how you want and in an equal way to other people who might have chosen another branded service to do the same thing.
If net neutrality were to go away, your internet experience would no longer be under your control. If you chose one supplier over another, your experience would be different.
If this was water, your tap would fill up glasses not bought from your own water provider slower than the glasses you might already have. If this was electricity, the devices in your home made by one company that was sponsoring your electricity supplier would work better than those devices made by a company that wasn't paying your provider.
With the Internet, the equivalent to your water or electricity provider is your ISP (Internet Service Provider) - this could be your home broadband connection or your mobile / cellular service provider for your mobile phone. These ISPs have the technical capability to speed up or slow down any content that they choose to.
To date there have been very limited cases of this happening, and regulations have been put in place to prevent it from happening in the future.
"Great!" you say. "It's Sunday evening Dax" you say. "We are good right?"
Neutrality is under threat in the USA from a reversal of protective regulation. And at this point, if you haven't already, watch the John Oliver video above, and then watch this update from him below.