Todd -
Normalizing is the same thing as adding gain. Basically, what normalizing will do is look for the highest peak, then determine how much gain is needed to make that peak 0dB (or -0.5dB or whatever you set it to). Then, that amount of gain is applyed to the whole file. So you add as much gain as possible without pushing any peaks into clipping and without losing any dynamic range relative to what you started with.