Dependency Injection is a way of injecting the dependencies into your class. Your class declares it’s dependencies (e.g. via a constructor parameter) and whoever is using your class can provide those dependencies. This way we don’t hard-code dependencies into our classes and our codebase is a lot more flexible.
React Native is a new native library that vastly changes the way in which you can create applications. The majority of the information and tutorials on the subject come from the angle of "you are a web developer, and want to do native".