requirement of current drive for MOSFETs
A MOSFET is a voltage-controlled device, but the gate has a capacitance associated with it.  There's a total amount of charge that you have to deliver to the gate to switch the device on.  You can see this on the data sheet as Qt.  The capacitances are listed as Cgs and Cgd.  The Miller effect will multiply the Cgd as you transition through the linear region.

Now, one of the advantages of the FET is that you can switch it very rapidly (for example to minimize switching losses).

In order to change the voltage on a capacitor quickly, you need to supply high peak currents, because I=C*dv/dt. If you try to switch a FET with a GPIO output with only 20mA of drive capability it will switch but much more slowly than it could.  

A FET driver can usually supply something like 0.5A to 4A peak currents to the gate to charge and discharge quickly.