Throughout Drupal, you will find the concept of a Teaser. A teaser is a short piece of text, usually the first paragraph or two of an article. This text is then displayed in most lists, including the default home page (/node). Many modules (including Views) are designed to work with node teasers, and the concept of a "teaser" vs the node "body" is integral to the workings of Drupal core and the Drupal UI.

The length of the default teaser can be modified. You will be able to change the number of words after which Drupal attempts to break the text cleanly. When the length of the content exceeds the set limit, a link to "Read More" will automatically be displayed. In Drupal 6, click Administer > Content management > Post settings.

In Drupal 7, the instructions are a little more complex, but you get more flexibility as this setting can be changed on a per-content type basis.

1. click Administer > Structure > Content types.
2. click the "Manage display" link for the content type you wish to edit
3. click "Custom Display Settings" to drop down its settings
4. make sure "Teaser" is enabled. Save the content type if you had to make a change.
5. you should see a "Teaser" sub-tab. Click it.
6. make sure the Format is set to "Summary or trimmed".
7. click the gear widget on the right side of the settings
8. set the trim length and click "Update"
9. click the "Save" button

Some modules help you to display different content, or different versions of that content in 'teaser' view vs full 'body' view. image.module for example inserts a thumbnail of an image into the teaser, while you see a page-sized version when viewing the node.

CCK provides many features under Administer › Content management > Content types allowing you to fine-tune what does and doesn't show as a teaser.

Teaser break

The length of the teaser can be overridden when editing the node content itself and allows you to choose a logical length for the introduction. In Drupal 6 the edit interface gives you the option to "Split Summary at Cursor". Using that button will visually divide your edit area into [teaser] and [the rest of the content].
Some of the Drupal contributed WYSIWYG editors also provide that feature in their own way when configured to do so.

Show summary in full view

When you first 'split' a teaser from the body content, it is still treated as part of the page when the full page is displayed. This is the easiest and most intuitive way for automatically-generated teaser text to work. A reader always sees [teaser] and [the rest of the content] without seeing any break.

For more control, better grammar, or to make the teaser text more promotional in nature when the first paragraphs on their own don't adequately describe the node, you can choose to not "Show summary in full view".

If you choose this option, the custom description will not be displayed as part of the full-text. Your full text should be complete, and make sense alone, and your teaser, which is used to entice readers to click "Read more" can be entirely different from the text that appears in the actual item.

Some more reading: Using teasers for effective SEO