A mechanical keyboard uses actual, physical switches underneath the keys to determine when the user has pushed a key. Press a key, and you press its switch down. Press the switch down, and the keyboard sends a signal to the PC telling it that you pressed that key.
At first, this design doesn't sound so remarkable. After all, you already have a keyboard, and you can tell when you've pressed a key: You push one down, and a letter pops up on the screen. Take a second, however, to think about how you know you've pressed a key--it's probably because you've pushed the key down as far as it will go, only after which do you see something happen on your PC.
Most keyboards are composed of a set of three plastic membranes, with rubber dome-shaped switches underneath each key. Press a key, and the rubber switch pushes through a hole in the middle membrane to connect the top and bottom membranes, which creates an electrical circuit that causes the keyboard to send the input to your PC. This keyboard design is inexpensive and spill-resistant, but it doesn't give you as much tactile or audible feedback when you press a key, which can change the way you type.