Your purpose in Fantasy Life, like in real life, will vary wildly depending on your personality, ambitions and desires. For the most part, it will involve performing various tasks to acquire Dosh, Bliss and Stars.
Basically money. The more Dosh you have, the more items and services you can purchase, which in turn will make your life easier.
Dosh can be obtained through hard work, such as by defeating monsters, completing quests or selling items you've looted or crafted. So far, so simple!
Happiness, in other words! The citizens of Reveria are a little... discriminating towards people who they don't deem "happy" enough and won't provide their services.
Bliss can be gotten by completing "Flutter's Requests", then exchanged for "Bliss Bonuses" by speaking to Flutter in your house.
These indicate your proficiency in a particular Life. Each Life has its own set of Stars, so when you change Life, your Star count will change.
You acquire Stars by completing Challenges specific to your Life; get enough Stars and you'll upgrade to a higher Life rank when you report to your Life master.
Saving the World
Besides the above, it is also your mission to restore peace to Reveria, by advancing the Story Quest (i.e. the main campaign).
At certain points in the game, after completing all of Flutter's Requests and receiving a Bliss Check, you can begin the next Story Quest by speaking to Flutter in your house.
Of course, being such an open-ended game, there are many more things you can look forward to and, with a little imagination, you can even create your own tasks and missions yourself!