Ordinary headphones convert an oscillating electrical signal into movements of the speaker diaphragm. This makes the air vibrate and, in turn, your eardrums. The eardrum is connected to a set of three tiny bones that amplify the vibration onto a smaller eardrum called the oval window.
But the oval window picks up vibrations from the skull too. When you hear yourself speaking, the sound reaches you through the air and also through your skull; that’s why our own voices often sound weird when we hear a recording played back.
Bone-conduction headphones use rubber speaker diaphragms that press directly on your head. Instead of vibrating the air and then your outer eardrum, they send vibrations directly into your skull.
Your head resonates at different frequencies to your eardrum so the headphones must shift the frequencies to compensate. The result is music that sounds as if it’s coming from inside your head!