Apparently this means something like 'the lookout' from its most recent use following a foray by hostile clansmen from another island who chopped off the thumbs of all the men so they could never again use a sword

It is evidently in origin a "galleried dun" of considerable antiquity having a mixture of characters of a burial chamber and a broch ( http://www.pbase.com/crisscross/broch ) about which little is known.
http://canmore.rcahms.gov.uk/en/site/21974/details/dun+a+gheird+mull/&biblio=more - it is evident that a lot of the original stone has been deliberately demolished and strewn down the east slope