Tor is a network which is designed to provide anonymity online, and protect you from online tracking.
There are a number of different ways to access Tor but, from a desktop computer, the most common way is through TorBrowser.
You can use Tor for secure file sharing (via OnionShare).
Tor is very easy to use and, if you use TorBrowser, you are unlikely to notice anything different, other than perhaps it taking a bit longer to load webpages.
If you want to circumvent a restriction on a local network, or browse without your local network operator seeing your traffic, Tor is a convenient, easy to use, way of doing it.
Although Tor is a tool which can help you with anonymity online, it cannot guarantee it. Nothing can.
In particular, on some devices — such as iOS — some protocols will still reveal information about you. These include WebRTC (used for in-browser audio and video calls), some media files, and visiting sites which have “EV” certificates (which show the company's name in a green bar in the browser address bar).
There is a stigma attached to using Tor — the moniker of the “dark net” — but, like encryption (used by criminals, as well us being essential for secure online activity) and cars (helpful for commuting; also used by some criminals as getaway cars, or driven by some in breach of the speed limit), Tor is neither good nor bad, nor is it used solely for bad things.
The fact that you are using Tor is readily detectable — it is not hidden at all — and, if the country you are in regards use of Tor as a sign of doing something wrong, or perhaps even having something to hide, using Tor may, in itself, be a risk.
You may find it harder, or even impossible, to access your chosen website via Tor. This depends on how the site operator has configured it.
Some sites try to detect “bad” traffic, and work out whether there is an actual user trying to gain access. To do this, they use “captchas” — those irritating “click all the squares which contain pictures of traffic lights” pop-ups which you need to complete.
Using Tor is a good way of having to do lots more captchas.
Tor works by wrapping your traffic up in encryption, and routing it through multiple different computers, with each computer stripping off one layer of encryption.
The computer in the chain with the slowest Internet connection acts as a bottleneck, and expect browsing to be slower than if you were not using Tor.
For most traffic, performance is likely to be acceptable, but using it for accessing videos is both frustrating and rather unfair.