Cranial Data, or Brain data, is an arrangement of scripts or code, or even full data, that is stored in a computer chip implanted within someone's brain.
It seems that cranial data is a normal medium used by Elysium's citizens (at least those like John Carlyle) to secure and protect extremely sensitive data for transport, similar to a modern-day flash drive, but far more secure. There also appears to be data defense programs, such as the Sabre Cerebral Defense program that John Carlyle uses to secure his code when he uploads it into his brain, that provides further security in case someone attempts to use the code in an unauthorized manner.
With cranial data, just like any other type of data, it is possible for people to implant devices into the brain that are capable of syncing and "grabbing" the cranial data from the individual. This action is referred to as a data heist, and is considered a type of theft. It is also hinted at in the movie that bank account codes and other financial security information is held in the cranial data bank, which would imply that the cranial data implant also functions as a security measure to authorize funds or even access to secured areas.