Short shift kits are a popular mod that serve two main purposes: firstly, because they shorten the distance that the gear lever needs to travel between gears - by reducing the angle that the shaft travels - the idea is that your quicker shifts will result in better performance. This is because less time is wasted on the shifting movement. In reality, though, the performance benefits will be negligible to most drivers.
The second (and most noticeable) benefit of short shift kits is the way they transform the driving experience. Even cars with already great-shifting gearboxes (MX-5s, GT-86s et al) can be made to feel even better, while cars with long manual throws - that make drivers feel like they’re stirring a pot of oats - are instantly given a far sportier, shorter shifting action.
Another key benefit is that cars with short shifters will be slightly more difficult to drive smoothly, especially if you’re not used to driving with a stick. If you’re an American with a short shifter, then your car’s damn near impossible to steal.
Here’s a great video on how to install a short shift kit…