What a time for a book about computers! Machines are faster than ever, with some systems clocking in at more than three gigahertz. Yet, amazingly, they cost less than ever before, too. You can buy a new personal computer for less than $300—at least if you turn over rocks for the best prices and look for a free operating system (which is sort of like buying a car and curb-surfing for tires). Source: The Winn L. Rosch Hardware Bible
Previous answers have cited sources that define but do not explain the term "leave no stone unturned"; it may be easier to remember with a bit of visual background:
Imagine that you are looking for a valuable coin that was dropped in a field ten years ago. You won't just look in every centimeter of the field, you will pick up every rock to look underneath it. Once you've done that, you have, literally, left no stone unturned.