Strictly speaking, all vacuum cleaners use magnets. Magnets are crucial to the electric motors that create the cleaner's suction. Some vacuum cleaners, however, are adapted with a magnetic device that removes metallic objects before they are sucked up.
Magnets in Motors
Vacuum cleaners need electric motors to work. Inside every electric motor are several magnets, including permanent magnets and electromagnets. The magnetic fields push against each other to create the force that drives the motor. The motor, in turn, drives a fan, which creates the suction that pulls dirt and dust into the unit.
Metal Objects and Vacuum Cleaners
Over time, every household appliance suffers wear and tear. Vacuum cleaners are no exception. Small dust particles and soft fibres don't do much harm to the internal structure of the unit. Harder items such as small coins, needles and other metal objects can also get sucked up into the cleaner, however, and these can cause a little more damage. By removing these items before they enter the unit, magnets can help reduce this damage.
Considerations
Not all metallic items are magnetic. Metals such as copper and aluminium are not attracted to magnets and therefore would not be affected by any kind of magnetic separation device.