One of the use cases of callback URLs is OAuth. Let us do this with an Instagram Login: If the user enters their credentials and clicks the Login button, Instagram will validate the credentials and return an access_token. We need that access_token in our app.

For our app to be able to listen to such links, we need to add a callback URL to our Activity. We can do this by adding an <intent-filter/> to our Activity, which will react to that callback URL. Assume that our callback URL is appSchema://appName.com. Then you have to add the following lines to your desired Activity in the Manifest.xml file:

<action android:name="android.intent.action.VIEW" />
<category android:name="android.intent.category.BROWSABLE"/>
<data android:host="appName.com" android:scheme="appSchema"/>

Explanation of the lines above:

Now, in order to get the contents of the URL in your Activity, you need to override the onResume() method as follows:

@Override 
public void onResume() { 
    // The following line will return "appSchema://appName.com".
    String CALLBACK_URL = getResources().getString(R.string.insta_callback);
    Uri uri = getIntent().getData();
    if (uri != null && uri.toString().startsWith(CALLBACK_URL)) {
        String access_token = uri.getQueryParameter("access_token");
    }
    // Perform other operations here.
}

Now you have retrieved the access_token from Instagram, that is used in various API endpoints of Instagram.