You are a singer and your voice is your instrument. You should know how it works and what it looks like, both anatomically and in motion. In the simplest of terms, and I believe in simplicity, the following is an overview of how your voice works:
You take a breath and your lungs expand. Think of your lungs as bellows or your power source. As you begin to make a sound, your vocal cords, which you can think of as your tone generator, are brought together. As air is pushed up from your lungs and through your trachea (windpipe), your vocal cords vibrate and produce a tone. Once a tone is made, it must resonate, or be amplified to be heard. The tone becomes amplified and modified by your nasal passages, upper throat and mouth. These areas are often called the "Resonators" you can think of the Resonators like the body of a guitar or a piano; that which makes the sound bigger, more beautiful. Finally, the tone must be shaped and propelled by the "Articulators". The Articulators are the tongue, pharynx, palette, jaw and lips and are used to form consonants and vowels, as well as the shape and depth of the tone.
So, there you have it, in very simple terms.
The diaphram is an important breathing muscle and much has been written about its importance in singing. Here is a link that will explain what it is and how it functions. http://wiki.answers.com/Q/How_does_the_diaphragm_function_in_breathing 
