A reed switch comprises of two ferrous metal strips that are encased in a glass tube filled with inert gasses. Naturally the two strips overlap but are set with a gap between them. This means that the circuit is incomplete. To complete the circuit, a magnet is applied to the switch, this causes the gap to close thus completing the circuit. When the magnet is removed, the strips are no longer attracted meaning they separate and then break the circuit.
In the circuit shown above, when a magnet is applied in the proximity of the reed switch, the circuit is complete thus lighting up the LED. when the magnet is removed the circuit breaks, turning off the LED.