It's more about adding javaScript to a webpage to enhance the functionality. The main reason I installed it was to stop esc from taking me out of full screen mode on Safari. Sometimes a website would open a dialog and when I pressed esc to close it I'd revert to windowed mode. Then I'd have to switch back to full screen mode. This solved that problem and I found some bonus features for a few sites I use.
Greasemonkey, Userscript Interface, etc is basically an interface that started as a firefox addon/plugin "GreaseMonkey" which allowed client-side personalizations to specified websites; from simple things such as changing a bit of CSS to suit the user's taste to scripts that alter an entire site.
Along with being able to personally alter websites, a few functions were added to the GM sandbox to allow for Cross Domain Requests, Local Key-Value storage, and other things of said nature that generally wouldn't be possible or could cause a security risk from within a page-style sandbox. From there, Google Chrome/Webkit incorporated the interface natively, and labeled said scripts as "Userscripts".
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I quite enjoy making my own greasemonkey/user scripts. I mean, everyone has that 'one tweak' they wish they could make to websites and GM/UScripts is the conduit to make such tweaks possible.
To see the entire GM API, and read more about it, check out: http://wiki.greasespot.net/Main_Page
And for scripts: http://userscripts.org
I guess I should mention here that differing browsers may only partially support the API. I know the developers of Google Chrome don't support some of the api due to security risks. Opera is slowly adding features, and safari, like firefox, only has access to it via plugins
What's NinjaKit?