RenderMan needs to know where to find the various external files that your RIB files may reference, e.g. textures, shaders, etc. MayaMan will automatically insert any necessary paths that it knows about, but if you need to add any additional paths you can use this dialog.
For all the tabs in this dialog, you can add a new path by entering it in the text field (or browsing to the location) and clicking the 'Add Path' button. Select an entry and click the 'Remove Selected' button to discard a path. Paths can be edited by selecting them (they will appear in the text field), making changes and then clicking the 'Apply Changes' button.Most of the time you will not need to enter any search paths using this dialog, as MayaMan should automatically put into the RIB files any necessary paths that it knows about. However, with advanced usage, in particular when substituting geometry with ReadArchive RIB files or using the Arbitrary RIB statement functionality, it is possible that you will need to pass additional paths to your RenderMan renderer.
In general, there is no need to add any paths to this dialog unless your renderer complains that it cannot find a certain file at render time.