This means that sharks are possibly able to shut off parts or most of their brain to "rest" while they keep swimming(seems similar to how dolphins will shut off half their brain at a time). Even then there are some places, such as the caves off of Isla Mujeres are places for sharks that dont normally stop swimming to stop and take a rest. read more
The idea that sharks will drown if they stop swimming is a common one, but it's not entirely true. There are two main ways sharks go about breathing. Ancient shark species breathed through a method called buccal pumping, which some of today's sharks still use. read more