I don't understand the windings inside my power drill.
The motor is a universal motor. It is so named because it can operate from either AC or DC power. The center rotating part is called the rotor. The outer stationary part is called the stator. The smaller diameter copper part on one end of the rotor is the commutator. Current flows through the stator windings and the commutator to the rotor windings. As the rotor moves, the commutator changes the connection of the rotor windings so that the magnetic field in the rotor is always at close to a right angle with the stator windings. That way the magnetic force keeps pulling the rotor around in a circle trying to align the rotor field with the stator field, but it can never catch up and just keeps on turning.

When a universal motor is operated from AC power, the current reverses 50 or 60 times per second depending on the power frequency. Since the current flows from the rotor to the stator, the current and magnetic field reverse in both parts at the same instant. That keeps the motor turning in the same direction even though the current keeps reversing.

To reverse the motor, the rotor winding connection is reversed with respect to the stator winding.

Since the universal motor has torque vs. speed characteristics similar to those of a DC motor, inserting a series resistance as with a rheostat works well as a method of speed control except for the heat generated in the resistor.