In Japanese, "Cardian" is written with kanji meaning "Hanafuda" and "Protection". The reading "Cardian" is a pun on "Card" and "Guardian". In English, the addition of the word "Flower" may reflect the fact that "Hanafuda" is written with kanji meaning "Flower" and "Card".
This archetype revolves around performing plays that mirror plays from hanafuda games. Their effects allow the player to Tribute the "Flower Cardian" monsters worth 1 point in hanafuda games on their field to Special Summon the monster of matching Level worth 20 points from their hand, which will then allow the player to draw 1 card. If the drawn card is a "Flower Cardian" who has another of matching Level on the field, the player can keep Special Summoning "Flower Cardian" monsters and drawing cards. This arrangement is meant to gather the right cards on the field to perform a combination named "Yaku", represented by a Synchro Summon.
The archetype uses cards such as "Flower Gathering" to gather cards more quickly. Everything revolves around gathering the right cards to perform a "Yaku" and Synchro Summon the Synchro Monster corresponding to that combo. By using "Flower Stacking" followed by "Super Koi Koi" it's possible to summon any Level 4 or 6 Synchro Monster, or a Rank 2 Xyz Monster.