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From the WikiPedia [en.wikipedia.org] article:
Greasemonkey is a Mozilla Firefox add-on that allows users to install scripts that make on-the-fly changes to HTML web page content [..] As Greasemonkey scripts are persistent, the changes made to the web pages are executed every time the page is opened, making them effectively permanent for the user running the script.
Typical use includes:
adding new functions to web pages (for example, embedding price comparison in Amazon.com web pages), fixing rendering bugs, combining data from multiple webpages