Physics professor Rick Matthews of Wake Forest University has some great pages to help us see the distinctions. His web page Digital Image File Types Explained is very informative and has great examples embedded in the page that demonstrate the differences in image clarity/quality as well as file size, too.
Designer and blogger Jennifer Farley published this article "GIF, PNG, JPG. Which One To Use?" that also does a great job of explaining the differences between the popular web formats, and with examples to demonstrate visually the quality (and transparency) as well as the file size.