Wikipedia is a good source of info here.
Basically a flyback converter is an isolated switching topology derived from the boost topology. With the boost, charging and discharging of the inductor happens on the same winding. With the flyback, the energy is put into the primary of the transformer while the switch is on and transferred to the output capacitor from the secondary of the transformer when the switch is off. During the charging phase, the switch is on and energy is stored in the magnetic field of the transformer. Then the switch is opened and the magnetic field collapses, transferring energy into the circuit connected to the secondary of the flyback transformer.
As I mentioned, the primary use of flyback technology is for isolation of the primary and secondary halves of the power supply. You can also obtain secondary voltages by having multiple secondary windings. Regulation is usually achieved with either an optocoupler or a small feedback winding which provides the necessary information back to the regulator so that it can maintain a constant voltage (the most common case) or a constant current in the secondary.
While always using the concept of a step-up (boost) converter, flyback converters can be, by using different winding numbers on the primary and secondary sides, built into regulators with a higher output voltage compared to the input voltage (step-up voltage conversion, but not a step-up converter topology), or a lower output voltage compared to the input voltage (step-down voltage conversion, but not a step-down converter topology), or both, and can supply multiple isolated output voltages, limited only by the input supply, switch and transformer. Since flyback regulators require a transformer, they are often more expensive than simpler non-isolated designs.