Fuel injectors are designed to accurately meter fuel to the engine and to deliver it in a precise pattern of extremely fine droplets. Because the fuel passages are very narrow, injectors are highly sensitive to even small amounts of deposits in the critical regions where the fuel is metered and atomised. These deposits can reduce fuel flow and alter the spray pattern.
Fuel needs to be finely atomised for it to burn properly, and an altered spray pattern can result in fuel droplets that are too large to be properly burnt. Although generally passing harmlessly through the exhaust system, the unburned fuel is clearly not producing power and the inefficient combustion ultimately means the engine uses more fuel to produce a given power output as a result.
Although less common than fuel injection these days, carburetted engines also experience similar problems from deposits because carburettors also use a number of small channels and orifices to meter and vaporise fuel.