Post format is a theme feature introduced with Version 3.1. A Post Format is a piece of meta information that can be used by a theme to customize its presentation of a post. The Post Formats feature provides a standardized list of formats that are available to all themes that support the feature. Themes are not required to support every format on the list. New formats cannot be introduced by themes or even plugins. The standardization of this list provides both compatibility between numerous themes and an avenue for external blogging tools to access this feature in a consistent fashion.
In short, with a theme that supports Post Formats, a blogger can change how each post looks by choosing a Post Format from a radio-button list.
Note that while the actual post content entry won’t change, the theme can use this user choice to display the post differently based on the format chosen. For example, a theme could leave off the display of the title for a “Status” post. How things are displayed is entirely up to the theme, but here are some general guidelines.