The orignal flash was Jay Garrick, he retired for a while in between and during this time Barry got his powers and since Jay was absent he took the mantle and became the second flash. Barry later takes on a sidekick, Wally, who goes by the name of kid flash but after Barry dies in the orignal crisis Wally becomes the flash to honour Barry's memory. In the current continuity all three of them are alive and share the title of the flash.
(Bart allen, the grandson of Barry also held the mantle of the flash for a brief while during wally's disappearance and became the fourth person to hold the title)