The support and flow of breath from your lungs makes the vocal folds in your larynx (or voice box) create vibrations. The vibrations, or sound waves, resonate in the space of your throat, mouth, nose (and to some extent your chest) and become your voice.
The TUC handbook Keeping well at work is available from the TUC publications online shop, priced £9.99, and explains how straining your voice can lead to serious injury and what you can do about it.