The content area is set up to display the "excerpt" if one exists, but it doesn't generate the excerpt automatically. You can either use a
<!--more-->
tag in the editor to force a break in the content, or you can enable the "Excerpt" editor on the "Screen Options" dropdown (button in the top-right corner of the editor screen) and create a custom excerpt.
I believe there are also quite a few plugins out there that will auto-generate an excerpt based on user-defined rules.
