TOR
TOR is one of many ways to use the internet without giving away your IP address, your ISP and hence your identity.
How it works is that a person loads software onto their machine which is called "onion proxies", onion being a name that uniquely belongs to TOR (it should not be confused with The Onion, a fake newspaper, although it is likely that that is the reason that TOR chose the name onion, as it gives fake IP addresses).
After loading the software, they run it, and then whenever they access anything on the internet it gives off a fake IP address. Anyone getting e-mails from them, any web site hosts, or anyone running any kind of internet technology will get a fake IP address (one which belongs to TOR) as opposed to their real IP address.
There is a way to find out who they really are, but only if you have the facility to snoop their incoming and outgoing traffic.
Ultimately, however, TOR owns a certain number of IP addresses, and individual companies can ban the use of those IP addresses, if they are concerned about trying to find out who someone really is.
For example, Wikipedia as of 2007 banned the use of TOR to access Wikipedia, so that they could more adequately enforce bans.
TOR was created with an aim to protect people's privacy from snoops, to stop stalkers and the like.
Naturally, TOR is often abused by people who want to engage in stalking, smearing people's names, or simply getting into places that they are banned from.
With the appropriate warrants, it is possible for police to require TOR to tell them who used what IP address, and hence to find out the real identity of someone who connected through their service. Therefore, using TOR does not guarantee that someone is unable to be prosecuted, although it does make it more difficult.