Basically, because they provide more tactile feedback. Rubber dome switches don't actually activate until after you feel the "click." If you're careful, you can push up and down on a key, feeling the rubber dome collapse/expand without actually creating an electrical connection. On a mechanical keyboard, the audible and physical click IS the keystroke. Immediately upon physical feedback, you've entered a keystroke and can lift your finger. You don't have to mash it like a rubber dome. The result is that your brain gets better feedback, sooner, and you can (sometimes) type faster. You definitely type with more consistent force and less strain.
Indeed. Those are buckling spring key switches, which aren't that common in the high end keyboard market anymore.
In my short research I found the geekhack forums and their wiki page on
keyboard switches. To sum it up, different switches are suitable for different tasks.
The Cherry switch company makes the switches that go in Filco (like mine) and many other keyboards, like the Das Keyboard (which is basically a modified Filco). There's three main types: Cherry MX blue, brown and black. The colors refer to the color of the stem on the switch (which is visible when a key is removed). The blues are very clicky (loud) and provide the best feedback for typing. The browns require a little less force, similar tactile feedback but without excessive noise (what I'm getting). The blacks require a bit more force and have a linear force curve, which apparently provides a great springy feel for gaming but isn't so great for typing. The MX black switches are in the SteelSeries keyboards, for example (which are probably made by the same company that makes Filco keyboards).
General consensus is that among the common Cherry MX switch types, blue is best for typing, black is best for gaming, and brown is somewhere in between, being good at both. One of the reasons blue is discouraged for gaming is that they're
loud and can be distracting while in a game. The brown switches like I got are much more quiet. You can find videos on YouTube to get a good idea of how loud they are.
Then they're the Topre keyboards, which have some crazy hybrid of rubber dome and mechanical spring. Apparently they accept multiple levels of force (they use a capacitative switch) while still providing a lot of feedback. They're really quiet and also provide what people say is the best typing experience ever. Unfortunately they cost $230. Probably worth it if you do a lot of typing all day long (like me) but I personally can't justify the money right now.
Then on top of all that there's other factors, like how the switches are mounted. Filco keyboards mount the switches on heavy metal plates, Das Keyboards mount the switches right on PCBs. They're supposed to feel a little different... the difference of banging on metal vs banging on fiber glass.
In short: better tactile feedback, less wrist strain, higher typing speed. Not to mention that a good mechanical keyboard is indestructible and will just about never wear out.
Bassoon, n. A brazen instrument into which a fool blows out his brains.