"Teasers" - short summaries of node content
Throughout Drupal you will find the concept of a "Teaser". 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.
Simply, a "Teaser" is a short piece of text, usually a paragraph or two that describes or summarizes the content. This summary is then displayed in most lists, including the default home page ( /node ).
The length of the default teaser can be modified by visiting Administer › Content management › Post settings and will attempt to break cleanly at paragraphs or words in the text. When the length of the content exceeds the set limit, a link to "Read More" will automatically be displayed.
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. The is highly recommended, as you can 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 contrib WYSIWYG editors also provide that feature in their own way, when configured to do so.
Drupal 5 offers the ability to manually enter a special tag to indicate where to split the content.
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 optionally 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 "more" can be entirely different from the actual item.