Not only them, we all move at the speed of light.
Photons are fundamental subatomic particles that carry the electromagnetic force—or, in simple words, they are light particles (and much more). Photon is also the "quantum" or fundamental unit of electromagnetic radiation.
We are all surrounded by photons: the light coming from TV, mobile and laptop screens is made up of photons, in X-rays, doctors see bones that are made up of photons, the radio in the car gets its signal from photons. And a fridge on magnets uses photons to hold itself.
They refer to themselves as photons because like all other subatomic particles, photons exhibit wave-particle duality, meaning that sometimes they behave as tiny particles and sometimes they act as waves. Photons are massless, allowing them to travel at the speed of light (opens in new tab) in a vacuum (299,792,4k58 meters per second) and can travel an infinite distance.
That's why they refers to themselves as "photon in a double-slit".