Tor is a system of encrypting messages from one person to the next. The internet is essentially like sending snail mail. You write a letter to an acquaintance with a request for a package, and they send you the package. We would be freaked out if someone was reading our mail and looking through our packages. We would be further freaked out if they were collecting this information into a database to learn more about us. And yet, this is exactly what’s happening on the internet. What we call “the internet” is actually millions of delivery routes between computers that request information, and the servers that deliver it.
“Tor” is actually an acronym for “The Onion Router.” Instead of sending messages directly to the server, it’s sent through a series of servers to the final destination. Your messages are encrypted 3 times before it sends, each acting as a layer of encryption, hence “Onion”. When a layer is decrypted by the intermediate server, called a “relay”, it contains instructions on where to send it next. The next relay receives an encrypted message, decrypts it, and then has decrypted instructions on where to send it next. This prevents any one relay from knowing where the message is going. The last relay decrypts the message and sends it to the final destination. So while the last relay and the final server know the message, they don’t know who it’s from. Even if the last server were collecting personal information, it would appear to be from a random person, potentially in another country.
It’s not perfect, there’s some ways around it. For instance, someone could own 100% of all relays, and then continue reading your mail. It’s unlikely, but it’s possible. It’s also possible that too few people use it. When too few people use it, someone can use process of elimination. I once heard an idea that if you get a license plate that says “l1l11l1” Then no one will be able to report you. It doesn’t work if you’re the only one with a license plate like that. Ideally, you get 1000 people with a similar license plate. Anonymity only works in large numbers.
Why do you need anonymity if you have nothing to hide? Because you might have something to hide in the future. If you only do illegal stuff when you’re anonymous, all the government has to do is catch you being anonymous. Don’t give them any clues! Be anonymous all the time. If only criminals are anonymous, then all the government has to do is arrest people who are anonymous. There may be a point in the distant future when you feel the need to rise up against your government, and you’ll need anonymity now, in the past of that future.