The figure below on the left shows the operation image. A rectangular wave is created by MOSFET repeating ON/OFF. This wave is applied to the coil. A desired DC voltage can be obtained by smoothing (averaging) this rectangular wave. The output voltage value is determined by the duty ratio of the rectangular wave.
As the figure below on the right shows, when the MOSFET is ON, current of the coil mainly flows through the MOSFET. At this time, energy is accumulated in the coil. The coil operates so as to release the accumulated energy and suppress the change of the current. When the MOSFET turns OFF, the current flowing through the coil will lose the path up to now. However, due to the property of continuing the current of the coil, the current flows through the diode and the capacitor is charged. This causes voltage exceeding the input voltage to be generated.