Welcome to the Community!!
In order for YOUR app to run on the devices, you must first download the AppSheet device container. This container bridges the gap between your app the device specific operating system. This is how your app is supported to run on ALL mobile devices - iOS, Android, tablets, etc.
Tap the install function again, you will probably notice that instead of “Install AppSheet” button the button will now read “Install App”. This will place your specific app on the device. You will likely be asked to save the App Icon to your home screen. This is optional and allows you to tap the icon to launch directly into your app.
There is an alternative way to get to your app. After you have installed AppSheet, when you launch it, tap the Menu on the left hand side. Mid-way down the Menu you will see an option for “App Gallery”. Tap this to see all of your apps, whether they have been downloaded to the device or not. Tap an app to download to the device.
One more thing, on the Menu below the “App Gallery”, there is an option for “Add Shortcut”. This is where you can add the shortcut Icon to your home screen for any app that you didn’t do so during the install.
I hope this helps!!