You may be seeing that title and wondering what it means. Well, it's just as it sounds: by taking advantage of a bug that lets you overwrite data in the game's memory, it is possible to write and run any code you want from within Pokemon Yellow. While this was performed on an emulator with automated button presses, it would theoretically be possible to do on an actual Game Boy.
Confused? The explanation can be found in detail here, but if you don't know much about programming it probably won't help you a whole lot. Basically though, there's a glitch that lets you mess with items beyond the twenty slots you're supposed to have in your bag. Once you do that, you're messing with data that isn't normally supposed to be messed with. Each item, pokemon, or anything else in the game has a numeric value. If you know what these values are, you can use them to change other parts of the game's memory to what you want. For example, in this tool assisted speed run, the glitch is used to change the destination of a door so that it warps the player to the Hall of Fame instead.
In the video above, this idea was taken to the extreme and by moving just the right number of just the right items to just the right places, the corresponding values in memory spelled out a program that could be run. In this case, the program was one that allowed you to write more programs by using button presses rather than item transfers, and displayed the input values on-screen. The end result? A program that displayed a picture of balloons and played a MIDI of the My Little Pony theme.