When you speak, the vocal folds in your throat vibrate, which causes your skin, skull and oral cavities to also vibrate, and we perceive this as sound. The vibrations mix with the sound waves traveling from your mouth to your eardrum. This tends to gives your voice a deeper, more dignified sound that only you can hear.
Through a loudspeaker or recording device, you pick up sound only through air conduction. The sound we're used to hearing has a lower frequency from the bone vibrations. Many people cringe at the playback sound because our brain struggles to accept that this foreign voice is our own.