This button is available only when you are not at the top level of a . You can tell you're at the top level when this button is unavailable and the name in the edit field matches the name in the Material Editor title bar.
A typical situation is one in which you have a material with a Diffuse map. The Material level is the parent and the Diffuse map is the child. The Go To Parent button becomes available at the level of the Diffuse map.