Chrysanthemum's core gameplay involves gathering seeds in the center of the World Bloom then venturing out onto its petal tips to plant the seeds and collect Guild Runes.

Guild Runes enable you to learn spells from the Card Drafting Area. With spells, you can plant and collect seeds at a faster rate, disrupt your opponents, travel across the World Bloom more efficiently, and exchange or enhance your resources. Using spells also increases your chances of finding a Bloom card, which causes the World Bloom to expand, giving you access to many new Guild Runes, spells, and places to plant seeds.

Additionally, being the player to find a Bloom card will give you an advantage by allowing you to take more actions than your opponents.

As for the Faerie Queen's reward...

...nobody knows what it is...

...yet.