A planetary gearbox refers to 
a gear system in which a number of ‘world’ gears rotate around a central ‘sun’ gear. Typically, a planet carrier is powered by the input torque which rotates the planets around a fixed outer ring (sometimes known as the annulus). This in turn drives sunlight gear which then provides the output torque. However there are examples of the other combinations, like the sun gear being set and the band providing output torque.
The main advantage of planetary gearboxes are their high power transmission efficiencies. Typicially this could be around simply 3% per stage. Further to this, the high effiency is delivered regardless of the compact design giving a sizable torque to size/weight ratio. A few of this is thanks to the load sharing occurring across the multiple planet gears.