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.