Can someone explain net neutrality to me?

I don’t get net neutrality and the wikipedia page doesn’t help:

“Network neutrality (also net neutrality, Internet neutrality) is a principle proposed for user access networks participating in the Internet that advocates no restrictions by Internet Service Providers and governments on content, sites, platforms, on the kinds of equipment that may be attached, and no restrictions on the modes of communication allowed”

…Uhh…what? And what’s all this stuff that’s happening with Google and Verizon? Can someone please explain this in layman’s terms? How about just kindergarten terms?