Let's go back to elementary school science. This is the visible spectrum - the light we can see with our naked eyes - but a small part of the electromagnetic spectrum.
This is the electromagnetic spectrum. It starts with gamma rays on the far left and travels to the right via X-rays, microwaves and radio waves. The tiny visible spectrum between ultraviolet and infrared is the only part of the spectrum that humans can see with the naked eye, unless OBAs are involved.
OBAs absorb a portion of the invisible ultraviolet light and re-emit it as blue light. This reflected blue light makes the fabric appear brighter and whiter.
Image courtesy of Wikipedia.