Coil formers are components found in a transformer(an electrical device that transfers energy between two or more circuits). They're commonly used in electrical printed circuit boards(PCBs) to produce the energy needed to power electrical machines such as motors and generators.
Coil formers are commonly used in transformers or as reactors in switch-mode power supplies. Transformers are used to bring voltage up or down in an AC electrical circuit. Both transformers and switch-mode power supplies can be used to convert mains AC power to DC power.
There are transformers all over every house. They are inside the chargers used to charge your mobile phone and other personal computing devices. They're also found in loudspeakers and microphones.