Greasemonkey is a very powerful tool, which allows you to fix website annoyances or add desired functionality missing from a site. Additionally, the scripts can bring content from other sites and resources and embed them into the page you are viewing. For example, you could create a script on that pulls the current Amazon.com price for a book when visiting a competitors site. You can use Greasemonkey to view Amazon's price right beside the competitors within the browser.
Just as musicians remix music to create new works of art, Greasemonkey allows you to remix web sites to create user experiences more valuable to you. Best of all, you can share these remixable snippets with others. Just be sure to remix responsibly -- violating the terms of service on some web applications can get you banned.