A material defines how light reflects off of faces in a group. This includes the color of the faces and a texture map. A group can have only one material applied. The same material may be applied to more than one group.
A material can be created using the Materials Window. You can open the Materials Window from the Materials menu, or by selecting one or more faces and then clicking the "..." button under "Group Materials" (note that you must have a group assigned to the faces for this to work.
Once you have opened the Materials Window, click "New Material..." and enter a name for the material. If you want to apply a 2D image texture map, click the "Set Texture" button.
Note that textures filenames in MM3D are saved relative to the directory in which the model is saved. It is a good idea to copy your image into the model directory or a sub-directory from where the model is.
If you are editing a texture file with a paint program while MM3D is running you can reload the texture using the "Reload Textures" option in the Materials menu.
When changing the material that is applied to faces using the Group Properties panel, be aware that changing the material for the selected faces applies this change to all faces in the group, not just the selected ones.
To change the way the texture is mapped onto the faces of the group you will need to move the Texture Coordinates. Sometimes using a Texture Projection gives you a good starting point for texture coordinate assignment.