The pitch of your voice is determined by the length and thickness of your vocal chords. Men have deeper voices than women because their vocal chords are longer and thicker. Children have the highest pitched voices of all because their vocal chords are short and thin. The vocal chords are contained in the larynx, or voice box.
You can see this by looking at stringed instruments; a cello has a deeper sound than a violin because it is larger, with longer strings, and the strings on a cello are thicker than those on a violin. Even on the same instrument, the strings become thicker as the sound deepens.