Tor is both a network and a system intended to allow users to be anonymous online. When you connect to the internet and request a page, a lot of things happen behind the scenes – and each one of them reveals information about who you are. Your IP address (and by extension your location) among other things are clearly shown to be requesting the pages you look at, and what you’re downloading and uploading, and so on. Tor is a way for individuals to browse and host content on the web with total privacy and anonymity.
Tor works by first encrypting the request the user wants to send, and then randomly sending it between several different tor nodes before finally reaching the destination server. Only the destination can decrypt the contents, which are then processed and the response is sent back in the same fashion. This is structured in such a way that the destination server has no idea where the original request came from – only the last node in the chain.
Due to this design, users of the tor network can communicate with various servers (such as browsing the web) without it ever being known that is in fact them. Of course, there are downsides as well. Tor has to encrypt as well as pass the data through a bunch of other servers before reaching it’s destination, which means it’s a lot slower than a regular connection. Also, the security of the network is entirely dependent on the security of the individual nodes – should they be collecting and storing private information there’s really no benefit to using tor.
Tor also provides the ability for servers to host content without the need for a public IP address (thus giving away the server location) using a .onion top-level domain. The tor network understands this domain type and routes data anonymously both to and from the server – the server itself actually being a tor client itself running a special configuration. However, finding these onion-based websites is difficult, as Tor is decentralized by nature, and there is no centralized list or directory of tor websites.
You can check out the Tor Project here.