Manipulating light
Bleach (specifically the optical brighteners in it) absorbs ultraviolet (UV) light found naturally in sunlight and some indoor lighting, and then re-emits it as blue visible light. This blue light counteracts yellow tones in clothing, making our eyes perceive the fabric as cleaner and brighter.
So: when a white garment starts to yellow from sun exposure or repeated washing, the extra blue light helps mask the yellowing – making the clothes look whiter and fresher, even though no actual dirt has been removed.