A native app is an app developed for a particular mobile device or platform (such as Android, iOS, or Windows). For example, iPhone apps are written in Swift, and Android apps are written in Java. Native apps are also better performing and have a high degree of reliability as they use the underlying system architecture and the device's built-in features.
Native apps can run in both the online mode as well as the offline mode. Native App is tied to the mobile operating system it has been developed for, and hence can't be run on any other operating system. This makes developing the native app costly as the same app has to be rewritten for another operating system. These apps are available to be downloaded on the mobile via the respective app store.
Here's an example of a native app. It's a news app bundled with iPhone and can be downloaded from the Apple App Store:
Another one is the popular Instagram app on Android phone, which is native: