Why In a depletion-mode FET the channel between source and drain is physically doped in during manufacture, so it conducts with zero volts on the gate. The gate voltage is then used to deplete (pinch off) that existing channel and reduce current, which is why it is called depletion mode. Most JFETs work this way, and depletion-mode MOSFETs exist too; they are described as 'normally on' devices.
Watch out The choice saying there is no current with zero gate voltage describes an enhancement-mode FET, which is normally off and needs gate bias to create (enhance) a channel. The mention of high electron mobility with no holes describes a HEMT, and majority-carrier holes just describes a P-channel device.
Depletion = normally ON, gate voltage takes current away. Enhancement = normally OFF, gate voltage builds the channel.