In AUTOCAD, what is the advantage and importance of layers and properties?

Layers give you more options to control the appearance, editing, and plotting of the drawing entities

In my modest experience, layer and properties allows you farther to extarct objects easily from your draw, or select them in order to make some change.

it is very easier to work in layers 

we can easily edit a particular layer 

customers can easily understand with the help of layers, to give deep knowledge about the project

The concept of layers is very important in AutoCAD and the correct use of layers can make your drawing much easier to work with. Basically, layers are the computer equivalent of tracing overlays on a drawing board. However, layers are much more powerful because you can have many layers in a single drawing and you can control the visibility, colour and linetype of layers independently. This makes working with very complicated drawings much more efficient. Layers are effectively a way of ordering your drawing. For example, you may need to create a number of construction lines in a drawing which will not form a part of the finished image. You could create a layer called "Construction" and use this for your construction lines. When the drawing is complete, you could simply turn this layer off so that it can't be seen. The beauty is that you could always turn this layer back on at some future time if modifications to the drawing are required. 

for me proper layer allow me to full control of my Layout(s) in paperspace with Layfrz command

and also agree in the2 previous answer..