I hesitated before I sent the long description of binoculars and cameras and how they work, but I knew that if I blew the technical details, my friend Dave Menough, who sold me those cool birding binoculars would be there to back me up. I could have asked him to explain it to me again before embarassing myself, but why do that? So, forget what I said before. Here is the real explanation:
"You are correct is saying that the 8 is the power, i.e. what you are looking at will be 8 times larger or appear to be 8 times closer. The other number, and here is where the nitpicking comes in, is the diameter of the objective lens, the lens closest to the object you are viewing, in millimeters. When dividing the power into the objective lens diameter one arrives at the size of the exit pupil. For instance, an 8X40 binocular would have a 5 mm exit pupil. The exit pupil can be described as the beam of light leaving the binocular end conveying information to the brain. Five mm is optimal, as one's eye pupil is about 5 mm under most conditions. Anything larger is wasted and results in unwanted weight. Anything smaller may not deliver all of the information the brain can handle."
I had part of it right. They're called binoculars. Right?