The Tor browser, one part of a software bundle created by the Tor project, is a more secure option to competitors such as Internet Explorer, Chrome and Firefox. Normal people interested in browsing privacy often use the Tor browser.
The browser, however, is just part of the bundle. What is left is there for people worried about cyberspying, those who want to evade censorship in some countries (e.g., a journalist in China), law enforcement who are working undercover, and, of course, criminals! Of course this makes using Tor for a normal person a problem because it raises flags for government agencies such as the NSA, which makes them more likely to target spying on you. And, if you’re doing something illegal, you are not so anonymous that you can’t be found with enough work on law enforcement/government’s work.
The Silk Road, not the trade routes of old in China and the Mediterranean, but an online anonymous marketplace operated inside of Tor is a perfect example of the illegal activity. It was shut down by the FBI in October 2013 but it was at one time was a place where you could easily purchase everything from illegal drugs to unlicensed firearms.
So, should you use it? If you’re just browsing the Internet and using social media outlets, probably not. It’s slower than its competitors because of all the jumping around it does to hide you. However, if you need a more secure option (e.g., using a public Wi-Fi at an airport) you may want to use it.