Question about Retopology

Hello… Could someone help me understand what is and how works Retopology?
how to use them in practical ways!

for example: If i sculpt something, why should I make the Retopology and after do this how can i still using my high poly mesh to apply materials and make other things?

A practical example :

You sculpt a statue, your goal is to have that statue in a game.
Now sculpts are going to be high poly, not good at all to be used as a game asset.

So you retopo to create a low poly version of your sculpt.
The low poly lose obviously the fine details of your sculpted statue, but it’s there that you’ll then use the baking process, normals, ambient occlusion etc… to fake the high poly detail into your low poly versions.
With a result that will stay low poly while making some illusion of high details, perfect as a game asset.

some pictures to see better what i mean

i have a sculpt made with dyntopo
http://i.imgur.com/vBHl1su.jpg

I then make a low poly retopo of it
http://i.imgur.com/Fv1mD5b.jpg

as you see it’s not very detailled, nowhere near the detail from my sculpt
http://i.imgur.com/jksjwYd.jpg

Now after some normals, ao and “dirty vertex” (to give a rough base texture too) baking, i can then fake the high poly details while the model is still low poly
http://i.imgur.com/YqUAn9B.jpg

There are plenty other reason to do that, by example in movie and animating, animating a sculpt is not really practical at all, rigging it is an immense headache and performance wise you’re going to have Blender explode :D, so retopo+baking will get you working

For baking, there are tons of tutorial around the net , here’s an old and very simple text+screenshot based one to see how it works :

Thank you! Very good explanation!!
but just to clear for complete!
then ,if I were to do an animation I would make a dense and detailed sculpture… then I would do Retopo, after that I would do the bake and my object would be in the end with the same quality?

Exact same quality, no.
But close enough to make illusion, if you retopo is well built (and not too low poly).

Thank you for your help!