Why is 18% gray used in photography, and what makes it special?

A very smart question!

This link tells the whole story.

It appears that the 18% gray value comes from the print world. On printed material, it's claimed that the half way point between black and white reflects 18% of the light. So a neutral gray (not whitish or blackish) is 18% gray. It very well may be that Kodak continues to market 18% gray cards because it is easy to produce and monitor this reflectance in production.

However:

Light meters are calibrated at the factory using ANSI standards. The standard has always been for a luminance value that is roughly equivalent to the reflectance of 12% gray.

And notice this comment:

[...] the 18% myth is so ingrained in the photography world that virtually everyone just parrots the party line. This includes Nikon USA, who will tell you that their camera meters are calibrated to 18% gray (talk to the Nikon Japan camera engineers, and you get a different story, as they'll respond "yes" when you ask if the Nikon meters are calibrated to ANSI standards; and yes, I had the chance to ask them a few years ago when I was in Japan).

So the answer is 18% is easy to reproduce in print, and light meters were either calibrated to true ANSI 12% and used some correction with the 18% gray or they were calibrated to 18%.

These days you take a 18% gray object and since RGB sensors sense the color, they can handle 18% gray easily. In fact, they can handle any gray if you only want to correct color - the brighter it is the better though, without overexposure, as more light allows for more precise metering. The reason why: the color space is being adjusted with this, but exposure is adjusted using the per-image metering.