Diffuse, in the simplest of terms, is essentially the color of an object. In reality, it is the color that an object reflects under pure white light.
The default setting in ORGE is full white, meaning objects reflect the maximum white light they can.
The diffuse setting has no effect if the ’lighting off’ attribute is used, or if any texture layer has a ’colour_op replace’ attribute.
Essentially, if you leave out the other light settings (ambient, specular, and emissive) and only play with diffuse, you can tint your object with different colors.
It is not required, since OGRE will default to the white diffuse if it's not specified.