Hi there,
Featured images can mean different things in different themes. In some themes, for example, you can add featured images to an image slider that appears at the top of your homepage. In your theme the featured image for the page replaces the normal header with the featured image header.
The small, medium, and large image size has to do with what size an image appears when you insert it into your page or post.
Please let us know if you have any more questions we can help you with.
Best!