Since the very very early days of the internet the de facto rule was something called 'network neutrality', the basic idea is that all traffic, regardless of type, source, or destination is treated the same. It's good, it works, and it's what consumers have demanded and ISPs have provided for the last 30 years or so.
Since the mid-90s certain groups have been trying to give the government more power to control and regulate the internet. It started in 1996 with the Telecom Act which was expanded in 2003, and in 2015 Obama's Administration signed a massive expansion of the FCC's regulatory power in what it labeled the Net Neutrality Bill. The bill is ~320 pages and grants the FCC unparalleled power to regulate ISPs, content providers, distributors, and user activity with only the broad guideline of 'encouraging a free and open internet' while leaving what that means entirely up to the FCC's interpretation and leaving the agency with minimal oversight in how it enacts its regulation.
The concern is that details and wording of regulations are incredibly easy for a new administration to change, while the powers that they grant are almost impossible to rein in once they come into effect. If a future administration decides that certain services or certain content aren't conducive to 'a free and open internet' there's basically no recourse short of a major shift in government to stop them from throttling or censoring those services and content or bringing fines and charges against those producing them.
tl;dr version - the Net Neutrality bill has about as much to do with network neutrality as the Patriot Act has to do with patriotism