Nearly all interactive, action-type games are written to run on a very specific speed of computer. They will not run correctly if the computer is too fast. Slowdown slows your computer down to simulate a PC/XT, PC/AT, or any user-configurable speed you desire. It can either be used to semi-permanently slow down your computer (to run several programs in a row), or just to slow down a single program (and the computer will automatically go back to normal speed when the program is finished).
Slowdown can also be used as a debugging/troubleshooting tool to slow down error messages long enough for you to see what they say.