If you zoom into a JPEG you'll notice some kind of blur... which is harder to express with vectors than a unicolor area. I'm no expert in these matters though. Take a photo with a tree and a lot of leaves on it - the resulting PNG might even be larger than the BMP since there are a lot of small areas with a lot of colors (even though they'll mostly be different shades of green =)) on the picture. Make a 1600x1200 rectangle and fill it with a single color, then save it as a BMP and as a PNG... the BMP will be a few MBs while the PNG will probably be a few hundred *bytes*.
It's not the best example but it's the only one I could come up with right now. :P