Long story short, SOPA and/or PIPA will give the US government the right to make it impossible to access a certain URL when you type it in your web browser. Furthermore, the only thing they will use to decide whether a web site should be effectively blacklisted from the Internet is if a copyright claim is made. Finally, it also includes not just offending sites, but any site that links to the offending site. And the worst part is the website in question gets no prior notice before they are basically kicked off the Internet.
So, to give an example, let's say you have an educational research website you've been running for five years. You use a 30 second clip of a Hollywood movie to make a point in a research paper, which is legal under the fair use policies according to US law. However, the MPAA claims your 30 second clip violates copyright. You get no notice of this claim, you do not get to argue your clip is not in violation of law, and you are afforded no due process. The government takes the claim from the MPAA and removes your website address from domain name servers, which means when I type in "http://sparkyswebsite.com", I will no longer be able to access your website. Furthermore, legally, Google could also be removed from the domain name servers, because their search result linked to your completely legal website, which the MPAA falsely accused you of violating copyright.
This is a completely awful law, which is a gigantic leap to censor the Internet, prohibit free speech, and exists only to cater to people like the RIAA and MPAA, because they've been bribing politicians for years.
