An asset is a template from which things in the game world are made. An asset instance is an object with a unique ID number, created from an asset. Areas are mainly populated with asset instances instantiated from the Asset Library. Assets own meshes.
A mesh is a single set of geometry, and a reference to the material which it uses. There may be multiple meshes in a model -- for example, a barrel of apples may consist of a mesh for the wooden barrel and a mesh for the pile of apples.
A material is a set of textures with defined roles (such as diffuse, normal/specular and macro) and associated properties. A material instance a unique combination of material properties which can be applied to one or more asset meshes. Material Instance Properties can be customized using the Material Instance Properties panel.