Some story events rely on precise timing. If you sprint past a trigger point at 6x speed, the game might not register that you entered an area. This can break quests.
Would you like a mock-up of how this could look in the settings menu or an example of the code logic for the speed memory?
In the context of emulation, a "speed up button" (usually mapped to the Spacebar on PC) allows the game to run faster than its native frame rate. Instead of playing at 60 frames per second (real-time), the emulator forces the game to run at 200%, 400%, or even 800% speed.