Noodletropin, a specialist in cognitive development and language acquisition states:

As others have noted, you hear sound from others only through the air, which gets to your cochlea through the ear and eardrum. When you are the one making the sound, vibrations reach the cochlea by propagating through your head (as well as the air). Bonus science: We do all sorts of things to manipulate sound before it reaches our cochleas. For example, your pinnae (the bumpy parts of your outer ear) shape and direct sound. So, if you use earphones, especially the in-ear variety, you should perceive the sound slightly differently than you would from free-field speakers. Even the shape of your head changes sound when it bends around your head. Some of these features allow us to localize sound in space.

Pratchett2, a specialist in neuroengineering states:

While there is some contribution to the discrepancy in the sound of one's voice as a result of damping through bone conduction, the major reason is actually something known as the pre-vocalization reflex. There's a great description of it here, but to summarize, essentially any time you are about to say something, cranial nerves fire in order to ensure that your hearing is dampened at that time, thereby making your voice sound different to yourself. If the function of these cranial nerves is harmed (Bell's Palsy), then you no longer hear yourself the way that you used to hear yourself. (Which is actually one of the symptoms for the disease).