Fikko3107 is correct, it is in fact a LEGO rubber band holder, for storing two different sizes of rubber bands. It's purpose insofar as the Bohrok sets are concerned, I'm afraid I don't know enough about Bionicle to give you an answer. Perhaps the instruction booklet may offer some clues?
As masterX244 stated, it is unofficially known as the 'nnenn' element, so named after Nate 'nnenn' Nielsen, who was a talented and prolific builder who used it as his Flickr avatar and who caused quite a stir among the LEGO community by using cut, painted and modified elements from clone brands as well as official LEGO parts. His build were so good, and so numerous, that despite offending purists and building brilliantly in a range of scales, he very rapidly became known as one of the better builders among the community - unfortunately, he was taken too soon from us all in a car accident and we will never see any new creations from this remarkable man, mentor, husband and father.
Fortunately, for those who never got to know nnenn's inimitable style, his Flickr account lives on and can be viewed here: http://www.flickr.com/photos/nnenn
He was also responsible for creating NoVVember (flickr.com/groups/921332@N22/pool/with/5203643999/), a month dedicated to starfighter builds based on the Vic Viper craft from the Gradius Series arcade shoot-em-up games (en.wikipedia.org/wiki/Vic_Viper).
LEGO (through the influence of set designer Mark Stafford) paid homage to his contribution to the hobby and the community by including his name on the Vic Viper inspired spacecraft that sits on the back of 7066: Earth Defense HQ (brickset.com/detail/?Set=7066-1).
His nickname is visible on the stickers, shown here: