Why does the road look like it's wet on hot days?

The phenomenon is called Mirage (EDIT: I called it Fata Morgana earlier, but a Fata Morgana is a special case of mirage that's a bit more complex). The responsible effect is the dependence of the refractive index of air on the density of air, which, in turn, depends on the temperature of the air (hot air being less dense than cold air).

A non-constant density leads to refraction of light. If there's a continuous gradient in the density, you get a bent curve (i) as opposed to light coming straight at you (d). Your eye does not know, of course, that the light (i) coming at it was bent, so your eye/brain continues the incoming light in a straight line (v).

This mirroring of the car (or other objects) then tricks you into thinking the road is wet, because a wet street would also lead to a reflection. In addition, the air wobbles (i.e. density fluctuations), causing the mirror image to wobble as well, which adds to the illusion of water.

Bend the light beam at the interface between a cold air mass with a mass of hot air as often seen in the mirage of the pavement.

As we look into the hot air region we see the light coming from the colder region, the sky, as metallic surface.

Physical explanation: The index of refraction of air exhibits a temperature dependence and makes the light rays bend more or less in the layer of separation of hot and cold layers.

It is a mirage: in particular it is caused by hot air near the road and less hot air above it creates a gradient in the refractive index of the air and so making a virtual image of the sky appear to be on or below the road. Air currents make this shimmer, similar to a reflection of the sky on water, hence causing the illusion of wetness.