The basic idea is that with Tor, you make HTTPS connections to the "tor relay", a network of volunteers who route your traffic around the world to make it hard to track. You can use Tor in two ways: you can join the relay network and route traffic for others, or you can just use the browser and make queries. If you do decide to join the relay network you have an additional decision about whether you will be an "exit node", one that does the final request to the destination website and thus appears to be the initiator of the request. This is an option because it can be difficult on home internet setups: if someone uses your exit node to post a lot of stupid crap to Reddit and Reddit tries to IP-ban them, then you are suddenly IP-banned from Reddit at home, because you ran the exit node.

If you are just a user then the only thing you need to know is that there is a price for your privacy, which is that routing your traffic all the way around the world takes a little more time than sending it straight to you, and this has two effects -- a latency jump which exists basically no matter how big the network gets, and a slowdown in your bandwidth which depends on how big the network is relative to the number of people trying to browse with it.