Pratt and Whitney Pure Power Geared Turbofan Engine Image 1
In most jet engines (more properly called turbofans), the fan that pulls air into the engine is directly linked to the compressor that squeezes that air down for combustion, so they have to turn at the same rate. Not so the in the Pure Power engine pictured here.
Pratt and Whitney Pure Power Geared Turbofan Engine Image 2
The gears in the Pure Power are placed between the compressor and the fan, which decouples the two, allowing for a more efficient arrangement: a big, slow fan shoving air into a small, fast turbine.