Currently, Internet Service Providers (ISPs) like Comcast, AT&T, Verizon, etc. are required to treat all data they serve equally. This is referred to as "net neutrality". It's the way the internet has traditionally worked, but several high profile cases (e.g. Comcast intentionally slowing Netflix to consumers in order to force Netflix to pay them more money in 2014) prompted the Obama administration to formalize this requirement by law in 2015.
The FCC wants to remove this requirement. This means there will be no restriction on how ISPs provide internet to you.
ISPs would be able to block content from you that they don't like (thinking of browsing a competitor's website, nope!), would be able to create paid fast lanes and slow your data down enough to force you to pay more, would be able to slow down Netflix, Hulu, and other apps unless you pay more money, and in general exert control over what you can and can't see on the internet.