JTAG (Joint Test Action Group) is originally a name of an organization which standardizes testing for semiconductor devices and PC boards. It also means the standards themselves which have been determined by the organization.
JTAG (Boundary Scan) test checks the connections between semiconductor device pins and footprints of a PC board which the device is implemented on. Each pin of the device has a JTAG register which stores the pin data. The registers are stitched serially, and the data come out from a special pin, synchronized by a test clock. And arbitrary data can be written to the registers as well. This scheme enables to check the connectivity between the device pins and the PC board.