This is the schematic of the LED maze. The implementation of the shift registers can be seen here. 3 inputs are passed to each shift register: clock, clear, and serial data in. Serial data in is used to decide which LED to activate, by using a binary representation of which LED to light. To light the 2nd and 5th led, for example, 01001000 will be passed to the serial in. Then, the clock is used to shift the serial data to it’s required position on each clock pulse. This is what results in the very dim LEDs showing up, as they are actually turning on for an extremely small amount of time compared to the LEDs that are meant to be on. Then finally, clear is used to make LEDs turn off again. This cycle repeats fast enough so that the LEDs meant to be on appear constantly on, and the other LEDs appear off (or are actually off).
This combination of inputs allows the control of each individual LED within the maze.