I like being able to customize my tools, partly because I'll want behavior that might not be desirable for others, but also because downloading and using someone else's code brings inherent risks.
User scripts are a way for folks to customize their browser, usually with small snippets of code that are easy to confirm are safe. Some browsers have user scripts built-in (Bromite comes to mind), and others can install an extension that provides user script support.
I've written a couple of my own scripts. They don't do anything amazing, but they are very useful for my day-to-day browsing.