Have you seen all the fancy new keyboards from companies like Logitech, Corsair or Coolermaster that claim they're "mechanical", cost double what a normal keyboard costs, and you're wondering what the hell is going on? Me too! After a bit of investigation, I can confidently say that you and I are living in keyboard ignorance, with our fingers crying out for a little more consideration and comfort.
The "mechanical", in mechanical keyboard refers to the way the keys on the keyboard work. When you push a key on a keyboard, what you're really doing is pushing two pieces of metal together in order to create an electrical circuit. The opening and closing of that circuit (the pushing down and releasing of a key on the keyboard) tells the computer which button you've pressed. Little do most people know, there are some wildly different ways to have two pieces of metal touch and those different methods are what makes each keyboard unique.
On most normal (aka cheap) keyboards, when you push a key, a rubber dome is squished under the key you pressed in order to create an electrical contact to tell the computer you pressed the key. On laptops and really thin keyboards, a "scissor" action (it looks like a little scissor lift, actually) is used to give those super thin keys a bit of depth when you push them down. Sometimes these are also called butterfly mechanisms.
Mechanical keys have the key cap resting on a weighted spring, that when pushed down makes a metal contact click together to register a keypress. Some of these mechanical keys also include tactile feedback via a bump that lets you know the key press has been registered. On top of that, there's some clicky switches that give additional feedback of a key press via a clicky noise.
But why mechanical?
What's so good about them though? All of them work, I can push the button and the letter appears: why spend hundreds on a mechanical keyboard? It's all about how it feels on your fingers and there's dozens of different switches around to please the pickiest of typists.
You might see in manufacturer spec sheets something like "Cherry MX Switches" - there are many manufacturers of keyboard switches that other manufacturers buy to install in their keyboard. Cherry, a German company, is probably the most prolific, right now. Alps is another popular brand, as is Topre. Cherry however, is the most popular, with dozens of different variations. This GIF has great detail on what each Cherry switch (MX Black, MX Brown, MX Blue, etc.) is good at, and explains how they operate with neat animations.
Many of the mechanical keyboards are aimed at gamers because there's advantages to being able to rapidly tap a key and have the key press acknowledged by the computer. Key rollover is another reason gamers like mechanical keyboards, as it provides the ability to press multiple keys at once and still have it register. It's pretty rare that you actually need to press six keys at once though.
People who just like to type and aren't gamers find mechanical keyboards to be much more enjoyable to work with, too. Less finger fatigue and a smoother action makes life easier for those who type a lot, such as writers or programmers.
This is just a basic overview of mechanical keyboards. There are massive communities dedicated to them and not just discussing different switch types, but full on customisation and very artistic keycap designs that look amazing. Reddit has a very active mechanical keyboard area and the Geekhack forum is full of mechanical keyboard nerdery to keep you satisfied indefinitely.