The double Blue glitch is a glitch that occurs in Pokémon Red and Blue.
Summaryif you use the Pewter Gym skip glitch to earn the Earth Badge, but skip the Boulder Badge, then a copy of your rival will appear on Route 22. The first Blue will speak to you (with under-levelled Pokémon) but then immediately act as if you defeated him. The game then hangs because the game is waiting for the other Blue to approach you, but he never finishes his path and instead waits at the edge of the screen.
This glitch works because when you defeat Brock, a flag is checked which removes the first Blue, and likewise when you defeat Giovanni, a flag is checked which adds the other Blue (with stronger Pokémon) to Route 22, so if you didn't defeat Brock, the other Blue is still there.