Greasemonkey is a userscript manager for Firefox. With the release of version 4, it has significantly fewer features than with version 3, and substantial compatibility issues with userscripts not specifically written to work with it. Greasemonkey recommends that you use some other engine.
If you choose to use Greasemonkey, keep in mind that a large number of userscripts do not function as intended. For userscripts commonly used with Stack Exchange, it's probably in the range of 75% of such userscripts are not functional with Greasemonkey 4. Most of the compatibility issues are ones based on intentional design decisions. Unfortunately, that means it's the developers' intent to not resolve the compatibility issues.
Most scripts should now use the tampermonkey tag, even if they target Violentmonkey or versions of Greasemonkey prior to GM4.