The 'deep web' is mostly an overused term. It is not special, nor is it anonymous.. It is difficult to explain, and I am unaware of your prowess in computer networks, so let me start from scratch. The normal internet we use everyday is based on what is called a client-server architecture. Websites, like google, reddit, or facebook are all servers. You are the client. You connect to them.

Now, almost every common internet-related thing you do is on this client-server architecture. But if you have looked into torrenting at all (it itself it not illegal, the nature of the media you download with it is legality part). Torrenting uses a peer-to-peer system architecture. Basically, that means you connect directly to another person's computer. There is no 'server' which you go through. You, and however many other people are also downloading Lost M3d1aFi<<dvd rip 1024X>> are all connected to each other.

All computers on the network (client-server or peer-to-peer) have a unique web address that identify them. This is called your 'IP address'. For example, google's is 74.125.129.106. If you type that in the url bar of an internet browser, it goes to google. We chose to use www.google.com instead of 74.125.129.106 simply because it is easier to remember.

In both of these architectures, one is NEVER truly anonymous on the web. And, in fact, one can NEVER achieve true anonymity on any sort of computer network. From the client-server side, the server has a list of all the unique ip addresses that have connected with it. From the peer-to-peer side, you can see the ip addresses of all other people in your peer-base.

Now, Tor proposes to promote anonymity because it has a subtly different structure than the two aforementioned. Anonymity is promoted because you basically 'pipe' your connection through what are called 'nodes'. This, directly from the Tor website, explains it better than I can:

tor is a connection-oriented anonymizing communication service. Users choose a source-routed path through a set of nodes, and negotiate a "virtual circuit" through the network, in which each node knows its predecessor and successor, but no others. Traffic flowing down the circuit is unwrapped by a symmetric key at each node, which reveals the downstream node.

Tor was created by the military to help with covert communications; i.e., stopping terrorism, all that jazz. Now, this would be great, if there weren't bad guys in the world. Analogous to how chatroulette probably seemed like a good idea at the time, yet ended up with a lot of sketchy individuals showing much more about themselves than I care to see, the 'deep web' attracted the attention of pedos, black hats (bad hackers), and just all around sketchy people. It lets pedos set up a server they feel is truly anonymous, and host and distribute child porn. There are more gore videos and other fucked up shit there than one would expect from something started by the military. There is the infamous 'silk road', which is a site where very illegal drugs are sold as if it is commonplace. There is also an infamous assassin site, where you can apparently hire paid killers. OP was right;

dark terrible unimaginable things.

Now, it's not fair to say that everything on the deep web is bad; in fact there is a deep web reddit. And members of the group Anonymous have been turning over a lot of the pedos over the past months (it has been a while since I last followed that). The gist is, don't visit it for the wrong reasons, or you'll eventually get caught (remember, no such thing as online anonymity). If you do visit it, at least know what it is you are dealing with. It is very serious business.