You use the material editor whenever you need to design the colour, texture, transparency, and other visual properties of an object's appearance.
Every visible surface has a material. You can make them shiny, dull, transparent, and opaque. You can texture a surface with an image used as its material's colour, or to lighten or darken its basic colour. You can also use a texture to control the transparency.
The lighting will also affect the appearance of objects in your scene.
Materials have a number of components. The main ones are:
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The ambient component is the colour of a material in a shadow. Normally you want it to be the same as the diffuse component.
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The diffuse component is what you would normally call the “color” of a material.
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The specular component is part of the “shininess” contribution.
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The emissive component represents light generated by a material.
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The rough component is the roughness of the material.
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Trans is the opaqueness of the material.
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The brilliance factor changes the appearance of the diffuse component.
Textures
While you can select basic textures from the materials dialogue, clicking the textures button will give you access to advanced textures.
There is a lot more information in the User Manual under Materials.

