Pruning "New Wood" vs. "Old Wood"

What does it mean when you are told that a shrub blooms on "new wood" or "old wood" and why is it important for a gardener or homeowner to know?  Flowering shrubs set flower buds and bloom either on "old wood", stems that grew during the previous year, or on "new wood", growth that is produced during the current year.  Shrubs that bloom on new wood in our area number only about forty compared to those that bloom on "old wood," which number over two hundred.  We are often asked by customers why a certain plant they own hasn't flowered, and sometimes the answer may be that pruning was done at the wrong time, so knowing when a shrub flowers tells us the proper time to prune to avoid cutting off the long awaited blooms.