Well, it's not the government that it provides censorship to, it's content owners. I'm going to copy an email I sent to my mom when she asked about this.
The bill in question, SOPA (Stop On-line Piracy Act), will "change the internet as we know it" depending on who "we" is. If you use the internet to surf web sites, email, and share pictures you took, then it isn't going to effect you at all. If you are a person that provides content, it may impact you. If you are a person that provides a facility for people to provide content, then you are heavily impacted. If you are a person that facilitates access for stealing other people's intelectual property, then you're going to hate it.
So, is this a bill you should support? No. It is a crappy bill, but it addresses a real problem. Like all legislation in the US, it is motivated by corporate concerns, and like all legislation motivated by corporate concerns, it over reaches in scope and intent. This one was motivated by pharmaceutical companies worried about "fake" versions of their drugs being promoted by on-line websites. Pfizer doesn't like it if you don't buy the officially sanctioned boner pills from them, after all, and the congressmen they own are there to help!
Right now the law grants to people who create stuff almost unlimited rights to distribute, re-create, or otherwise control the stuff they produce. As a guy that writes software and writes songs (the two big areas impacted by law) I think that's pretty important. There is a small army of degenerate thieves out there that believe they have a right to other people's stuff. They upload movies and songs and software to websites so other people can download it, which is a violation of the rights of the dude that actually created the work. So right now the law holds the people that upload and download this content accountable for it. You may have heard horror stories about the RIAA suing 12 year old kids for sharing songs, those evil bastards. What you don't hear is that poor 12 year old was sharing the entire Sony catalog and costing them millions in sales.
Now, when we say our little shit 12 year old was "uploading" we tend to overlook where he was uploading too. There are companies out there that do nothing but host websites for other people. Netflix, for example, is hosted almost entirely by Amazon. So if I'm a hosting company and I have literally thousands of websites on my computers, am I responsible for the content that our little shitbird uploads? Right now the law says "no" and provides some indemnity to me for his actions. If I find out about it and do nothing, then I have liability. If I don't actively protect against such things, then I have liability, but otherwise it's our turd-bird punk that is going to jail for it, not me. That is all well and good and reasonable.
SOPA would change that, and hold the hosting provider liable regardless of their knowledge of such things. That isn't right, which is why the bill is a bad one.
If you take a look at the list of companies that support SOPA, they are almost all companies that generate on-line content that is stolen and re-distributed without their consent. They have a right to be pissed, and I support their efforts to crush the little bastards that steal their shit. If you look at the list of companies opposed, they are almost universally companies that provide places on the internet for content to live. They have a right to be concerned, as this law would expose them to massive liability and the result would be less content, or content provided only by organizations that can afford the lawyers. Small hosting companies would assuredly be sued out of existence. The problem the law addresses is real. This isn't the right way to address it, though. It would mean Amazon was responsible for what Netflix does, which is unfair to both Amazon and Netflix.
This isn't a 1st amendment issue. There is no free speech when it comes to someone else's stuff. This is an Article 1 Section 8 issue. It involves balancing my right to control my material with liability for the people that inadvertently help facilitate its theft.
Short story: You shouldn't support it, but don't freak out.
Someday we'll win this thing...