Gate drivers and the half-bridge
A half-bridge, two MOSFETs stacked one above the other, is the basic unit of motor drives and converters. Why the upper switch needs a driver.
A half-bridge puts two MOSFETs (high side and low side) in series between supply and ground and uses the middle as the output. Only one of the two is on at a time, tying the output to the supply or to ground.
Why the high side is harder
To turn on an N-channel MOSFET, the gate has to be about 10 V above the source. The high-side source is the output node, so when it is on it rises to the supply voltage (for example 48 V). The gate then needs 58 V, a voltage an MCU cannot produce.
Bootstrap
A gate driver IC charges a small capacitor to 12 V while the low side is on and the output is at 0 V, and when the high side is to be turned on it stacks this capacitor on top of the source and uses it as the gate voltage. So the output has to come down to 0 V periodically, and 100% duty cannot be held for long.
Shoot-through and dead time
If both MOSFETs are on at the same time, the supply is shorted and they burn in an instant. Between turning one off and the other on there is a short time with both off (dead time, usually a few hundred ns). The advanced timers on STM32 insert this dead time in hardware.