The 'Exclude User Agent' box allows you to exclude from the stats all visits coming from visitors with a given user agent.
The user agent of a visitor is the software he is using to navigate your site. Typically an operating system and a browser with their version numbers. You can get the full user agent of any visitor by hovering your mouse over the browser or OS column of the visitor details report.
Typically this is used to exclude unwanted visits from things like robots or spider. The Yahoo spider for instance will show 'slurp' in its user agent string. Entering 'slurp' in the User Agent Exclusion box will therefore exclude any visitor whose user agent contains the word 'slurp'.
Other popular exclusions are the Google Preview (google web preview) or MSN preview robots.