A texture is a 2D graphic that is put onto a surface of a three-dimensional object, such as a face or an entire 3D object. Aside from simple filling colors, textures are the only thing that makes a three-dimensional object actually visible. Without any kind of filling these objects are only a mesh that by itself consists only of elements, that have no surfaces that could be visible to the player. For practicability reasons the meshes are still depicted of a collection of edges, but in an actual game usually the faces limited by them are filled with a texture or color.
There are different kinds of textures. Some of them are meant for direct display as a surface. Some are meant as a height-map for a surface. Usually they are using grey colors to indicate the height to be simulated on top of the object they are placed on, e.g. the whiter, the higher, the darker, the lower. Textures can have an alpha channel, giving them transparency values independent of the actual colors of their pixels.
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