A shift register is a clock-controlled logic circuit for storing and shifting binary data. It consists of a series connection of several flip-flops, each of which forms a single storage element and can only store and output one bit.
The data is applied in parallel to the inputs of the shift register, as bytes or nxBytes. So you have eight inputs or a multiple of them. The data stored in the shift register can be shifted from one register to the next register via the bit clock. With each bit clock the data is shifted one register further to the right. The byte clock takes care of writing the data into the registers and reading it out.
Shift registers are used as parallel-serial converters. In this case the data is read out serially with the byte clock. A further conversion of the serial data into parallel data corresponds to a serial-parallel conversion.