The idea is simple enough: you sign up for a Rovio Account using only your e-mail address, then your game saves will sync across your devices. There is even a nice feature that will let multiple users sync their saves using the same account, which is great for shared devices. The problem is that right now the Rovio games that offer the feature are very few.
Rovio Accounts can only be found globally in The Croods, and in the original Angry Birds for users in Finland and Poland. Rovio has promised to roll out the feature to more areas in the future, but there's no way to tell when that could be happening.