Dark and bright fringes are formed due to interference.
Dark fringes are formed by destructive interference where the waves are out of the phase.
Bright fringes are formed by constructive interference where waves are in phase.
Thomas Young demonstrated the phenomenon of interference through a double-slit experiment.
In this experiment, two slits are illuminated by a monochromatic source of light and a pattern of interference was obtained having dark and bright fringes.