Disney pools are themed or have special slides/features and are located in a central area of the resort. A quiet pool is a plain pool off in a less central area.
Not a themed pool. No slide, or pool bar with drinks and snacks. Usually in a quiet area of a resort. Here's a link to a picture of the quiet pool at the BWI: http://www.allearsnet.com/acc/bw42.jpg
While staying at The Villas of Wilderness Lodge I must have refered to the quiet pool once too often, my 4 year old nephew told me he want to go to "The Talking Pool."
As others have already stated, its a secondary smaller pool at some of the resorts, though the name "quiet" may not be entirely appropriate. At times it can be very noisy.