Here you can enter a name for the object.
Tracks will be named according to their animated parameter name by default. You can, though, rename your track to anything you like (Tarzan, Jane, Mike, Mary, etc.). If a R is located next to a name, this means that it is an auto-relative F-Curve, i.e., the F-Curve in the F-Curve mode has been moved for display purposes and the keys shown no longer reflect the Real Key Value.
If an element was assigned to a layer its layer color will be displayed here. This field reflects the layer color in the Layer Palette. You can drag & drop layers from the Layer Manager or similar layer fields onto this field. You can also assign layers or remove elements from current layers using the menus located behind the small triangle.