Electrical circuits
Electricity only flows around a complete, unbroken loop called a circuit, and a switch works by closing or opening that loop.
A worked example
A bulb lit by a battery needs an unbroken loop: wire from the battery to the bulb, through the bulb, and back to the battery. Cut the wire anywhere, even on the return trip, and the bulb goes dark.
The mistake people actually make
A broken loop anywhere stops the flow, not just a break next to the battery. Many students picture electricity only needing to reach the bulb, not return to the source.