Internet is very vast and what we use on daily basis is only a chunk of it. The Internet is much more than that but first, one should be clear with the difference between Internet and the Web.
Internet is the collection of various smaller networks where each node can be a server, laptop, smartphone etc.
Web : In earlier days of Internet, data was used to transfer across the Internet but no Web existed at that time but in 1989, Tim Berners-Lee introduced the World Wide Web which can be used to access hyperlinked text or web pages. So, basically Web is a software which runs over internet to provide this service.
But Web doesn’t include only the website like Facebook, Google, Geeksforgeeks etc. These are in the surface web which can be indexed by search engine. It only constitutes 4-6% of the whole web. Part of the WWW which is not indexed by a search engine like Google is Deep Web and it about 500-600 times larger than surface web. This web can only be accessed using a special link and with special permission like data in our cloud drive cannot be found on Google, one cannot search for it. There is a subset of the web called Dark Web.
Deep Web : It is the web which cannot be accessed by the search engines, like government private data, bank data, cloud data etc. These data are sensitive and private, so kept out of reach. It is used to provide access to a specific to a specific group of people.
Dark Net : It is a network build over the internet which is encrypted. Darknet provides anonymity to the users. One such darknet is Tor (The Onion Router). A special software is required to enter this network like Tor browser, is required to enter into the Tor’s network. TOR can access regular website also, a website on this network has .onion address. Many hidden services are provided on Dark Net.
Friend-to-Friend is another kind of darknet where two-person transfer data between them anonymously. Only concerned people have access to it and it is encrypted and password protected.
Freenet is also a darknet which is used for file transfer anonymously, there are many other darknets available.
Dark Web : Darknet provide a user with anonymity but a service was introduced which allowed someone to host a website on the darknet and remain anonymous. This attracted people who do illegal stuff to sells things without getting caught. One example is a website called the silk road which was on darknet called TOR, used to sell drugs and was taken down by FBI.
It might seem a bit scary but darknet is very useful too, for which it was created, to provide anonymity like to government official, journalist and even us.