This button is available only when you are not at the top level of a compound material. 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.