Colour perception is achieved by three types of cells in the retina of the eye called cones.
With the three types of cones, one is more sensitive to red light, one is more sensitive to blue light and the other is more sensitive to green light. Each cone reacts at different speeds to light and keep responding for different lengths of time. You only see white when all three cones respond equally.
The alternating white and black flashes on the disk cause the cones to respond at different times and lengths, leading the brain to
believe it is seeing coloured light.