Why are they so sought after? First, we must turn to what a mechanical keyboard is. I am not talking about what they are, their technical specifications or their advertising. I would like to recognize what the redeeming qualities of mechanical keyboards really are. I am typing on a Logitech G610 Orion Blue, which has Cherry MX Blue switches. This is important, as switches make quite the difference in the typing experience. The polar opposite of mechanical switches are membrane switches. They are the ones found in your average office keyboard that costs the grand total of 10 bucks. Never mind, they are fine and one can type on them. That is because they have never tired a mechanical keyboard. Once you've tried one, you will never forget that there's a whole other world, a community of enthusiasts, making and experimenting with mechanical keyboards. I personally only have experience with Blue switches, meaning that they are “clicky”. That also means they are loud. The travel is long compared to a membrane keyboard, and much more comfortable. It is really amazing. When you press down on the keycaps, you can feel the actuation point, the point in which the key registers to the computer. You know exactly where and how to press the key so that the timing is perfect. This is tremendously important to gaming, as each keypress can mean the difference between life and death in-game. Now, you might think: I know when my key registers to my computer in a membrane keyboard! Well, not really. For Blue switches, there's around a millimeter of travel from the key moving to the key actuating. I don't know why, but it just feels so much better.
Mechanical keyboards are good, but they are not cheap. A good, full-size mechanical keyboard from a trustworthy manufacture would set you back around 70-100+ dollars. However, I believe that it is worth it. These keyboards feel much better and would last longer than your 10 dollar keyboard. People correlate mechanical keyboards to “gaming keyboards”, but that really isn't accurate. “Gaming” things can be important, but they are generally a way for the companies to charge more on a product. My keyboard is marketed as “gaming”, but I almost never use it for gaming, and it works just fine. “Gaming” keyboards can be good, however. For example, most gaming keyboards have software that come with it, allowing for macros and key binds to be put in place. I have also seen SteelSeries keyboards have variable actuation points. These are all good things about gaming keyboards. I don't really have anything bad to say about gaming keyboards other than the issue that manufacturers overuse the term in marketing. Yes, almost all “GAMING” keyboards are mechanical, but some are cheap and are marketed as “mechanical feel”. They are cheap, but they aren't mechanical. They are just more stable mechanical switches with more travel. I'll end it here. There you have it, not really all that complicated. If you want to know which keyboard switch is right for you, search it up on google and take a small switch quiz to find which is right for you.
P.S. Cherry MX is the gold standard for switches. Buy those if you can (Unless you know your key switches really well).