Excerpts (teasers) can be shown on WordPress through two methods:

The first, keeping the the_content() template tag and inserting a quicktag called more at your desired “cut-off” point when editing the post.
The second, by replacing the the_content() template tag with the_excerpt().
In both cases, if you have set anything in the Excerpt meta box on the post editor screen, that text will be used. Otherwise, the excerpt will be automatically trimmed.

The most commonly used method is the first one, because the user editing the post can choose between showing the whole content or just the excerpt, individually for each post. However, using the_excerpt() in your template file can also get a teaser from the first 55 words of the post content, without the need to place a more quicktag in the post