When you first install the app but haven't yet logged in to your Zombies, Run! account, any workouts you perform will only be stored on your phone and not backed up online.
Once you log in to your Zombies, Run! account in the app (e.g. by tapping More > Zombies, Run! Account), workouts will automatically be backed up to your online account.
If you log out of your account in the app, you'll still be able to see all of your workout logs and other app data, but any changes will not be synchronised to your online account.
Please Note: A Zombies, Run! account is the only way to save/backup your data. We do not automatically back up your account details via Apple or Google or create a save file on your device. If you want to make sure your data is saved we'd strongly recommend creating a free account.