It's a module that attaches to the ECU of fuel-injected bikes. The PowerCommander is but one example; there are other similar products available (Yoshimura EMS, FactoryPro TEKA to name a few).
A stock bike's ECU (engine/electronic control unit) will have its own built in mappings for fuel delivery, optimized for the stock intake (airbox) and exhaust systems. These stock mappings usually work "well enough" -- if you keep the bike stock.
Once you introduce other variables into the intake/exhaust equation (e.g. higher-flowing air filters, full exhaust systems) the stock mappings no longer provide optimal fuel delivery to match the increased flow of air. End result is an air-fuel mixture that is too lean -- i.e., too much air coming through per unit of fuel. At best, a lean mixture will result in power loss at mid and upper RPMs. At worst, it can lead to engine failure due to overheating. (Running too "rich" -- too much fuel -- is better/safer than running too "lean".)
This is where a PowerCommander (and similar products) come in. These are programmable units that allow the fuel delivery (and in some cases, ignition timing) to be tweaked in order to optimize the air-fuel mix, and therefore, optimize the power band. On the PowerCommander at least, the fuel delivery can be minutely tweaked all across the RPM range. The programming can be done by a trained technician with the bike on a dynamometer, creating a custom map for that particular bike; or, widely available standard maps are available via download for common bike/modification combinations (e.g. "2004-2005 Suzuki GSXR600 with Yoshimura full exhaust"), which can then be uploaded to the unit via computer and USB cable.
Bikes tend to come from the factory with the stock ECU fuel delivery slightly on the lean side (for emissions and fuel economy purposes), so even a stock bike may benefit from these modules.