When you write code in Expo you are writing React Native code. Expo has two main pieces:-
Expo CLI (expo-cli): a developer tool for creating projects, viewing logs, opening on your device, publishing, etc.
Expo client: an app on your phone that lets you open your projects while you're working on them, without needing to go through XCode or Android Studio, and also lets other people view them too! And if you publish it through expo-cli, people can access it at any time through the Expo client on Android or on iOS if signed in to the same account it was published with. Lastly, we also make it possible to build standalone apps so people don't have to use the Expo client to open it, and you can distribute to the app store and play store if you like.
So Expo is a set of tools built on top of React Native. These tools depend on one key belief held at Expo: it's possible to build most apps without ever needing to write native code, provided that you have a comprehensive set of APIs exposed to JavaScript.