A common connector for plugging in a standard pair of music headphones such as the ones found on music players, computers and most other electronic devices with audio outputs.
It can support stereo and/or microphone, depending on the number of separate connector rings on the jack.
Some phones offer only a 2.5 mm jack, which is a smaller variety of the same principle.
Headphones supplied with mobile phones usually have a mic somewhere along the cable and a remote button that allows for managing calls without using the phone.
Some manufacturers opt for placing a 3.5mm audio jack on this remote control instead of directly on the phone itself. The reason for this is that 3.5mm jacks take up quite a lot of internal space; plus, in this way the user gets to keep the remote control/mic functionality while using third-party headphones.