If your device runs on Android OS, you can download applications with the .APK format. However, you must allow downloading from unknown sources, from your device's settings. Open Settings > Security and enable the Unknown sources option.
If your device runs on iOS (iPhone - iPad - iPod touch), most applications are available on the App Store. But it is possible to install applications outside the App Store by downloading a configuration profile. You can see this page for more information. (Configuration profiles are not available from all developers. If you are a system administrator, visit this page on how to install custom entreprise applications).
If your device runs on Tizen OS (Samsung Z model), you can download applications with the .TPK format. But as Android, you must allow downloading from external sources. Go to Settings > Security, and enable the Unknown sources option.