The human voice is produced by air from the lungs moving over the vocal cords in the larynx. The cartilaginous larynx is situated in the throat, below the tongue and above the lungs. The vocal cords themselves are formed from a combination of muscle and cartilage.
As they contract and relax, the space between them increases or decreases, which in turn changes the tone and pitch of the voice. However it is the force and speed of air passing over them which dictates the volume of our voices, and this air originates from the lungs.
So when you want to speak loudly, you take a deep breath in to fill your lungs before expelling the air rapidly and forcefully over the vocal cords.