One pound of muscle and one pound of fat are NOT the same size.
If I place one pound of muscle on a scale and one pound of fat on a scale, they will both weigh one pound. The difference is in total volume. One pound of muscle may appear to be the size of baseball; one pound of fat will be three times the size and look like a squiggly bowl of Jell-O.
Why is it that we can lose sizes, yet the scale remains the same? Because muscle weighs more than fat...
Muscle is a denser tissue and thus takes up less room than an equal weight of fat. That's why it's possible to lose inches but show no changes in scale weight. Having more muscle means you have a more desirable body composition, or fat-to-muscle ratio. You may still weigh the same, but your body will look different, smaller, better and tighter. Though it may take you a few weeks to see measurable changes, you begin to put on muscle and burn calories from the moment you start exercising.
The muscle weight you gain also beefs up your metabolism which in turn, helps you to burn off more fat. Talk about a win-win situation! (You won't jiggle as much at your ideal weight, either.)