In addition to what the king said just to clarify some of the terms: root can basically be thought of as the Linux equivalent of a Windows Administrator: a user with the highest privileges, an out of the box android distro from a major manufacture will block access to this to prevent you using your own device however you want

APIs are application program interfaces, you can think of them as software libraries full of useful functions and data structures for interacting with other software and data, examples are those used to interact with web platforms programtically(i.e bots such as the Amber one on here, use the lemmy API to read and make comments)

To learn more there's plenty of tutorials and such that can be found with a simple search, but if you want to gain a deeper knowledge the best thing I'd say is to mess around with running linux to learn about root

Or for APIs learning to code and you'll also pick up other associated knowledge and skills

Shizuku is an app that lets you use root functionality on an OEM locked phone, the GitHub is probably a good place: https://github.com/RikkaApps/Shizuku