Oil catch cans are simple devices that can greatly benefit direct-injected engines. They prevent oil and other contaminants from causing buildup inside your engine's intake manifold. Here's how they work, and why you might want to install one on your own car.
A typical catch can plugs into a hose running from the top of your engine's crankcase to the intake manifold. This hose relieves pressure in the crankcase generated by blow-by (when pressure escapes the combustion chamber by seeping past the piston rings). The problem is, this pressure relief hose allows oil and other nasty stuff from the crankcase to get into the intake manifold, where it doesn't belong. These contaminants can build up inside the intake; when left unchecked, this buildup can hurt fuel economy and horsepower, and can even cause misfires.
Why does this specifically affect direct-injected engines? Well, in port-injected engines, the fuel being sprayed into the intake works as a cleanser, washing off any oil buildup that might occur. Since direct injection engines shoot fuel directly into the cylinder, there's nothing preventing gunk from building up.
An oil catch can acts as a filter, plugging into this hose line to "catch" the contaminants before they can reach the intake. As Jason Fenske of shows in this video below, even a budget catch can is better than nothing. The only downsides are figuring out how to mount one under your hood, and remembering to empty it every now and then.