The game automatically saves your progress to your device.
However securing your account allows you to save your progress outside of your device, meaning that if your device is lost, you can log in on a new device and continue your career.
If you have not yet secured your account, you can do so in a variety of ways via the settings menu and tapping either:
Login with Facebook
This will tie your account to your Facebook profile.
Sign in with Apple ID
This will tie your account to your Apple ID, which will let you continue your career across multiple devices.
You can only secure your account with one of the two securing options at the same time, but you can swap that security method at any time by tapping “Manage Account”.