A magnetized watch will likely run slow or fast even after being cleaned and could become erratic when worn on the wrist.

Despite original claims of being anti-magnetic and made up of non magnetic alloys, vintage watches are prone to becoming magnetized over time. Magnetization puts strain on the components in a watch and causes a push and pull effect when there should be a smooth uniform operation.

Demagnetizers are a cheap way of fixing this. 

Pressing down the red button on the demagnetizer place the watch onto the device and slowly pull the watch away.

Your watch should now be demagnetized.

How easy was that!