Well, a brief description of procedurals (as I am a coder).
Procedurals are pieces of code that, in general, handle rendering of a graphical effect (often times in 3d games), instead of using prerendered artwork to create the effect.
For example, in 3d games, most particle / smoke effects, as well as waves (in a liquid) are procedurals, rather than using textures to create the effects. (Using textures to create smoke: think of old FPS games like Duke Nukem and Doom, where weapon impacts were just sprites drawn on the screen whereever the projectile happened to hit).
Mirror image effects can be done using procedurals as well.
Instead, a piece of code is used to produce the effect. Like the description said, it uses input (information from the environment) to create more realistic effects. (This is why, in 3d games there can be a reflection of the player/items behind him in a mirror or pool of water, because a piece of code handled the generation of this effect).
A closer-to-home example of a procedural would be in Outpost 2.
Most of the weapons fire in OP2 are just bitmaps stored in OP2_ART. When the game wants to show the weapons fire for a weapon such as the Rail Gun, it just uses the bitmaps from OP2_ART (in this case, the blue torus-shaped projectiles from the rail gun) and draws them in the correct place, to show the fire from the rail gun.
However, the laser, microwave, and thor's hammer fire are all procedural effects, as well as the 'glowing unit' when a lightning bolt hits a unit (either from the Thor's hammer or from a lightning storm). This means, there are no bitmaps for these graphical effects, they are rendered using a piece of code. (Albeit, these effects are pretty simple)
You might notice how they are 'semi transparent', you can see part of the terrain / unit below the weapons fire. This is due to procedural effects, as they can perform the alpha blending. (OP2_ART bitmaps have no alpha blending support, only basic sprite support (transparent/opaque))
EMP of any sort (both from the weapon, and from other events like a tokamak explosion) is not procedural however. It uses sprites from OP2_ART. Acid cloud also uses sprites (every other pixel in the cloud is transparent, in a checkerboard pattern, so it's possible to see through the cloud)
Anyway, hope that answers some questions.