Excerpts in WordPress are created via a couple different mechanisms.
First is via the Excerpt field found on the post editor. If the post author enters content into this field it will be used as the post excerpt.
Second is by a WordPress theme calling one of the excerpt functions such as get_the_excerpt();
Third is by referencing the <!–more–> tag within the post content itself.
Excerpts are most commonly used by site authors to display more summaries of the provided content while still staying cognizant of valuable real estate space. Excerpts are most commonly used on home pages, news feeds, article archive pages and so forth.