Don't panic, we know what to do.

Clear the cache and data of the Google Play Store application:

Head to the Settings => Apps => All window.

Find the Google Play Store application and click on it.

Click on the "Force Stop" button.

Use the "Uninstall updates", "Clear Cache" and "Clear data" buttons.

Restart your device, wait for 10 minutes and open the Google Play Store application.

Try to update/install the application one more time.