A launcher (I think it comes from app launcher) is usually the overview part where you have the apps and widgets and the wallpaper. Installing another launcher will let you change how it looks. The difference between most is how you can customize them. The default launcher only has basic customization, which can be more than enough for most people. Customization options can include icon size, icon shape, icon notification badge, app drawer, dock, icon themes, folders, gestures, and others.
This is just the traditional understanding, which a launcher doesn’t have to follow to be a launcher.
A clear benefit to using a different launcher is being able to change the experience you have.
I recommend you just search for launcher in the play store (or on f-droid if you’re feeling funky), and just give some a shot, just to get an idea of the differences.
The launcher I use and recommend is Nova Launcher.
Widgets don’t have much to do with a launcher because they’re supplied by the apps. I don’t use them much, but a calendar, weather, and search bar are the ones I have, all pretty useful.