Does anyone know what the crowns are for?
They are a measure of your progress. The learning is the same as it was been before the update. You do lessons, aquire Skills and Crowns. You learn a language. Some people are upset because the "game" changed. People who are here to learn a language either aren't bothered by the new format or like it better, like me. Others disliked it at first, then after trying it, came to like it more than the previous version.
Just treat crowns like you'd treat levels. They're an indicator of what level you reach in a particular skill. Level 1 (Crown 1) is the lowest and Level 5 (Crown 5) is the highest.
The Crown levels progress in difficulty as you go up them in terms of sentence complexity and number of exercises to complete. Eg. Level one may only contain 10 exercises, Level 5 might contain 50.