Tor (The Onion Router) Browser hides your action and place online by routing all of your surfing through multiple anonymous servers, thereby concealing where you are and making it challenging (although not impossible) to spot who is doing exactly what online. That means it is a good way to access websites that repressive authorities do not want people to see, for whistleblowers to report corruption and illegal action without getting fired or worse, and also to access the deep web.
The deep web is an internet over the internet, not indexed by search engines, and websites end with the .onion suffix and may only be accessed through Tor. As you'd expect, a few of those websites are key for perfectly good reasons - they're sharing information that somebody, somewhere does not need shared - however others are key because they're fantastically prohibited. Browse at your danger and keep in mind that Tor Browser makes it difficult to locate you, but does not offer 100% unbreakable anonymity. In reality, only using Tor can flag you as a individual worth watching, and it is banned on several people networks.
There are loads of legitimate uses however, and not only if you are a political activist. Tor may provide you internet access as soon as your internet provider's DNS servers are kaput, and it may continue to keep your surfing free of the advertisements trackers that infest numerous websites.
Tor Browser looks like Firefox and works like Firefox -- because it's Firefox. It is not too fast, however: onion routing makes all of your traffic move around considerably more than in a normal browser, that slows things down substantially.
It is important to realise that Tor can not protect you from dangerous behaviors, so by way of example if you run plugins from the browser they might influence Tor's capacity to protect your privacy. It is imperative that you don't submit information to websites that don't display a green or blue button from the browser address bar to signify that a secure https connection, for example.