Otherwise known as the "split-screen level" or a "kill screen", the Map 256 Glitch is, when you make it to map 256, the right side of the screen turns into a jumbled mess of numbers and letters and the left side is normal. It is impossible to beat. In Ms. Pac-Man, the screen goes blank with nothing except Ms. Pac-Man and the ghosts appearing. This also happens in Jr. Pac-Man, except there are bits of the sprites of the houses and balloon in the cut-scenes. It also occurs in the Pac-Man Google Doodle as an Easter Egg. There is even a game based on this glitch.
Why It Occurs
The level counter in the original Pac-Man is stored as an 8-bit integer, meaning the highest value it can hold is 255. However, a bug in the game's programming causes the level counter to "roll-over" to 256, resulting in an integer overflow and causing the game to attempt to draw 256 fruit to the screen. The result is the garbled mess on the right side of the maze.
The game checks for 244 Pac-Dots eaten by Pac-Man for the level to end. The right half of the screen contains only 9 dots. 122 on the left half plus the mere 9 on the right half is 131, not nearly enough to progress. (The nine dots can be consumed again on each life, but you can't get enough lives to make it to 244.) This also explains why Ms. Pac-Man's kill screen doesn't automatically progress to the next level despite the lack of dots.