Never mind... it is simply the field selection frame... I used to drag and drop the material, but I discovered that I can simply click on the material in the material window and the selected thumbnail takes it.
When there are two thumbnails (two sided face) you can select none, both, or only one of them and It makes sense, but when there is only one thumbnail if you select it and click the material on the material window it takes it, otherwise it doesn't! ... that puzzles me (because the object is already selected).