Daguerrotype !!!

When was it first discovered and by whom? 

Discovered by Louis Daguerre in 1984

What is special about the technique? 

You can only make one.
Light goes through it so it looks 3D.

How does this technique work/process?    Everything in italics from Wikipedia

1. Plate Preparation: a polished copper sheet is plated with silver (by Sheffield plating, or, later, by electroplating); this is then polished to a very high gloss.
2. Sensitisation: the plate is placed in an iodizing box and exposed to iodine vapour until all the surface silver has been converted to silver iodide, turning the plate orange. This is the light-sensitive coating. This had to be done shortly before the exposure, as iodized plates would rapidly degrade.
3. Exposure: The plate is loaded into a camera, and an exposure made simply by removing the lens cap. Exposures in early cameras could be over twenty minutes, even in bright daylight! However, this was less than some other, earlier processes. In 1840, Englishman John Goddard showed that sensitivity could be increased by using bromine, as well as iodine; this, together with improving lens technology brought times down considerably. Petzval's lens in particular brought typical apertures down from ~f14 to ~f3.5 - four stops improvement, i.e. potentially 16 times shorter exposures.
4. Development: the plates, kept in the dark, are suspended over a bath of mercury, which is heated to 60°C (140°F); mercury vapour forms an amalgam with the exposed silver iodide.
5. Fixing: unexposed silver iodide, not amalgamated with mercury, is washed off the plate using a salt (sodium chloride) solution (later replaced by weak sodium thiosulphate solution). This leaves the mercury/silver amalgam highlights and shadows of the original silver as a permanent - but delicate - image.
6. Toning: Original Daguerreotype images were extremely delicate, and could be marred by even a slight touch. In 1840, French physicist Hippolyte Fizeau (1819 – 1896) discovered that a heated gold chloride solution could both reduce the fragility and improve the tone of the image.
7. Mounting: The plate was usually sealed into a glass-fronted frame to protect the fragile surface from being scratched, or oxidising (tarnishing to black, as silver cutlery does) in the air

The camera obscura and a pewter plate coated with bitumen. Niepce called his picture-making
process heliography ("sun drawing"), but although he had managed to produce a permanent
image using a camera, the exposure time was around 8 hours. Niepce later abandoned pewter
plates in favour of silver-plated sheets of copper and discovered that the vapour from
iodine reacted with the silver coating to produce silver iodide, a light sensitive
compound.

Can you comment how important this technique has been for the history of photography. For example was it popular and is it still used today?

It was the first practicable method of obtaining permanent images with a camera.
Can you find Image evidence of the technique? 

Can you comment how important this technique has been for the history of photography. For example was it popular and is it still used today?

People dont use this technique no more because from 1839 till now the camera technology has dramatically changed.

Also you can only make 1 photo so it didn't come in handy if you want another one exactly the same.

Only specialist use this process