The ISP side: Internet Service Providers (who sell dial-up, DSL, cable modem connections, etc., e.g. "Verizon") have been finding that a huge amount of their bandwidth has been consumed by people ("Us") accessing a small number of "content providers" (websites, video-on-demand, etc., e.g. "Google"). This made the "Verizon" want to charge more, somehow, for access to those sites. Rather than charge their customers, there has been talk of charging "Google". If "Google" would refuse to pay, then access to "Google" would be restricted or slowed.
The User side: We pay "Verizon" for a connection to the internet. Gone are the days of Prodigy where the same company controlled everything. "Verizon" uses words like "internet access", "unlimited", and "always-on" to sell their services to us, and if they cannot afford to provide the service that they advertise, tough. Charge more and see what happens to your business. We don't care about a relationship between "Verizon" and "Google", as long as we can do our searches when whe want to.
Besides, doesn't "Google" already pay for internet access? Well, yes, but the internet is structured like a heirarchy. "Google" pays their ISP's and their ISP's pay the backbone providers for access. But, there it stops. Money only flows upwards, but the data goes both ways. As the data comes back down the heirarchy to the user, the connections are paid for by the user only! So the backbone upgrades can be potentially paid for by "Google" (negating one of the the arguments against net neutrality), but "Verizon" just has to accept their own revenue stream.
ISP's have always gone after the heaviest users and told them to tone it back. It makes business sense. Identify your biggest controllable expenses and try to eliminate them. First it was downloaders, then file sharers. But now it seems like *everyone* is using a lot of bandwidth. They can't attack all of their customers, or they'd get hit with false advertising lawsuits. Besides, ask RIAA, that doesn't work well. So they try to find out what all of these users have in common, where the data comes from, and attack there. Unfortunately, in the end, it's still us, the users, who are going to suffer as long as the ISP's are allowed to discriminate between "Google" and "Yahoo".