The “dark web” refers to websites which are not accessible via the normal internet. The Tor network allows access to a dark web of .onion websites, but other dark webs exist which are unrelated to Tor.
Accessing the dark web is completely legal. There are many benefits to using something like Tor Browser to access the dark web, such as increased protection against tracking. However, criminal activity does take place on the dark web, and using the dark web for criminal activities is illegal.
The deep web is a common term for pages which can’t be found easily by search engines, think of private social media accounts, paywalled content, or other sites which need an account to access. The dark web is a network of sites which can’t be accessed on the regular internet at all, you need to use special tools like Tor to access dark web sites.
Dark web networks like Tor are used by a wide variety of people including journalists, activists, minorities, and many other groups for perfectly legitimate activities. Sometimes, anonymously posting information to the Tor network is the only safe way to share information. The dark web is also used for criminal activity.