In short, yes, almost all the functionality in Meanings requires an active internet connection.
Meanings determines your next review in real-time, so you must be online in order to complete or receive new reviews. In addition, vocabulary data is stored on our servers so you can access it anywhere–this means adding, editing, deleting (and so on) vocabulary requires internet access.
We may explore an offline mode or functionality in the future, but there is nothing planned at this time.