I think that's backwards - the turbo button (very unintuitively) actually slowed down the computer to allow backwards compatibility with older software and games!
A lot of games didn't work properly if turbo mode was engaged. They would run unplayably fast, have crazy game breaking visual glitches, or just crash. A few of my games had a splash screen reminding the user to turn off turbo mode. The turbo button was mainly there to speed up processing for mundane tasks like spreadsheets or for compiling code.
It was basically to downclock the CPU because old computer games were built to run off of the speed of the CPU. When processors got faster those games scaled up their speed too. Normally you’d leave turbo on all the time except when playing those games. You turned it off and it would restrict the clock speed on the CPU.