This button is available only when you are not at the top level of a compound material, and there is more than one map or material at the current level.
A typical situation is one in which you have a material with a Diffuse map, a Bump map, and a Glossiness map. The Material level is the parent and the Diffuse map, Bump map, and Glossiness map are its children. Go Forward To Sibling becomes available at the level of the children and allows you to go from one to another.
You can also navigate through the levels of a material with the Material/Map Navigator.