This is most likely your "Exceprt" area. See the_excerpt.
The excerpt is created from the first 55 or so words of your post automagically by WordPress.
You can also use the "More" tag ...
<!-- more --> ... when editing your post to tell WP when to cutoff your exceprt text.
Also, depending on your theme, you can use/fill in the "Excerpt" box when editing a Post to specify the exact words you want WP to display when showing the Summary/Excerpt of the Post.
You can read on the Excerpt page linked above about how to customize the Excpert length to be any number besides 55 words if you are wanting to do that.
I hope this helps.