Definition
The dark web is an encrypted part of the internet that you can't find with ordinary search engines like Google, and you can only get into it by installing a special dedicated browser. Unlike the regular web, it's designed to hide the identity of both the visitor and the server.
The three layers of the web, seen as an iceberg
You can picture the internet we use every day as an iceberg floating in a huge ocean. The tip of the iceberg, which sticks out of the water where anyone can easily see it, is the surface web. Ordinary websites and news articles that pop up right away when you type something into Google belong here.
But under the sea hides a far bigger chunk of ice than the part above water. Places that don't show up in search, but that you enter with a password, like your email inbox, your bank account history, and private cloud storage, are together called the deep web. Most of all the data on the internet actually belongs to the deep web.
The dark web is a special zone hidden at the very bottom of that huge deep web. You can't just click a link to get in. You have to use special software that thoroughly hides your location and your traces.
How does it hide who you are?
On the regular internet, it's like sending a letter with the sender's address (the IP address) and the recipient's address written right on the envelope. If your internet provider or a server administrator wants to, they can easily trace when, where, and which sites you visited.
The dark web, by contrast, uses a path encrypted in many layers, like the skin of an onion. Your data passes through several relay computers scattered around the world. Each computer knows only the address of the computer right before it and right after it, and can't know where the data first started or where it's finally going.
It's like putting an envelope inside an envelope, with each courier tearing open only their own outer envelope and handing the rest to the next courier. That's how very strong anonymity is created: the server operator doesn't know who the visitor is, and the visitor can't know where the server really is. Still, there are several cases where a user's mistake or a security hole exposed someone's identity to law enforcement, and the operator was arrested.
A bit more precisely
Because of the name "dark web," it's easy to assume it was built for crime from the start. But this technology was originally developed in the 1990s at the U.S. Naval Research Laboratory to protect intelligence agencies' communications. Later it became widely used in authoritarian countries for press freedom and personal safety. For whistleblowers and journalists who dodge surveillance to tell the truth, it's like a lifeline.
But people abused the fact that it's nearly impossible to trace, and dark markets appeared where all kinds of illegal activity happens, such as drug dealing, trading illegal personal data, and selling malicious software. In effect, anonymity turned into a hideout for criminals.
Also, just getting on the dark web is often not illegal in itself. But if you go in out of curiosity with no protection, your computer can easily get infected with a virus, or you can get scammed. With no safety net, it's a dangerous space full of traps. Keep that in mind.
Common misconceptions
The deep web and the dark web are the same thing, and both are collections of illegal sites.
The deep web means all the web pages that don't show up in search (email inboxes, company intranets, bank account lookups, and so on). It's an everyday, legal area. The dark web is only a tiny, special part of the deep web that you can reach only with a special encrypted browser.
Where you meet it
A journalist in an authoritarian country with heavy press crackdowns uses it to tell the outside world what's really happening, without the government watching.
It's also abused as a hidden black market for trading illegal hacking tools or buying and selling leaked personal data, because of the anonymity.
In one sentence
The dark web is a secretive part of the internet that uses special software to encrypt the route in many layers, hiding the location of both the visitor and the server.