Shortcodes is a WordPress-specific code that lets you do nifty things with very little effort.
Shortcodes can embed files or create objects that would normally require lots of complicated, ugly code in just one line. Shortcode = shortcut.
For example, the following shortcode would add a photo gallery into the page:
Shortcodes can be with additional attributes as the following example shows:
[gallery id="27" size="medium"]
WordPress does offer some of the shortcodes by default (for example the gallery one) and plugins can add their own as well via the Shortcode API.