At least 2, almost certainly 3, and I'm not sure if or when you'll reach a hard limit.

The 365 license allows installation on multiple computers but you can only use one at a time. Macs and Windows machines require separate licenses.

The Activate this Computer screen will pop up each time you try to run the app on a new machine, and you'll need to be connected to the internet to make that happen. Otherwise, you only need to be connected once a month so the app can verify an active subscription.