You don't need the internet to play most of the time. There are, however, times when you do need an internet connection such as:
1. When you are setting up your myOsmo account.
2. When you are downloading or updating your Osmo apps.
3. When you are syncing up your game progress in myOsmo.
4. When you are creating custom albums for the Words app or downloading other people's albums.
5. When you are using the search feature or the sharing feature in the Masterpiece app.