They could be used to read minds, control them, and add information into them (news or a daily joke, for example). They were also the alternate universe's alternative to iPods, Mobile phones and music players.
Secretly, however, EarPods could remove information from a subject's brain by producing two metal prongs that met at the top of the head. (TV: Rise of the Cybermen) EarPods induced trance prior to "upgrading" of humans into Cybermen. The EarPods in the alternate universe took control of people by inducing a trance, but on the Doctor's Earth, the earpieces were drilled straight into the victim's brain. (TV: The Age of Steel)
When the Cybermen entered the Doctor's universe, the earpieces of the Torchwood Institute, specifically Torchwood 1, allowed control in a fashion similar to EarPods, paving the way for the Battle of Canary Wharf. (TV: Army of Ghosts)
During their attempted conquest of the Doctor's version of Earth in 1851, the Cybermen made cruder versions of the EarPods to control four workhouse owners. When the workhouse owners were no longer of use to the Cybermen, Miss Hartigan activated a switch which caused their EarPods to electrocute and kill them. (TV: The Next Doctor)