Native Apps are real genuine apps for iOS or Android that have been written in Swift or Java respectively. They are not cross compatible and must be written separately, but they can both connect to the same database. A native app offers the best experience for the user. Depending on what the app will do you don't necessarily need to be online to use it. A native app can use all the functionality that the device has, including touch id, location services, accessing contacts and gallery and using the accelerometer. The only limit you have with a native app is your imagination.
Pros and Cons of Native Apps
Offers the true app experience.
Is specifically tailored for Apple or Android devices so a person instinctively know how to use it.
Can access all the devices abilities including: fingerprint or camera logging in, location services, accelerometer, accessing a phone's contacts.
Fast and responsive
Can be more costly than hybrid apps.
The same app needs to built twice, once for each platform
Separate prices for Apple and Android versions of the same app.
Takes much longer to develop than Hybrid Apps.
The Android app will look slightly different to the iPhone app due to the nature of the operating system.