I really don't get what those are, and what they are used for. I've been using the manyus in upgrading characters, but the bloom dragons don't seem to contribute much to the upgrades anyways. Honestly don't know if I'm using the manyus correctly, but I'm pretty sure that the dragons serve some other purpose.
Help please thanks

The Dragons are used to evolve characters. If you go Units -> Character Evolution, you can select a character and see which dragons you need. Also character has to be max level to be able to be evolved.

Manyuu's are to used to level characters, they give bonus exp if the type of manyuu matches the Type of girl, the 4 colours that they.

Lv.5 Manyu's should be used to upgrade girls between level 1-20.
Lv.20 Manyu's should be used to upgrade girls between level 20-40.
Lv.100 Manyu's should be used to upgrade girls above level 40.

If you use a Lv.5 Manyu on a high level girl, it will cost way more gold so definitely avoid that! I personally use Lv.5 Manyu's on girls up to level 30.

2* girls need 1 Lv.20 Bloom and 4 Lv.5 Bloom to evolve.
3* girls need 3 Lv.20 Bloom and 2 Lv.5 Bloom to evolve.
4* girls need 1 Lv.100 Bloom and 4 Lv.20 Bloom to evolve.
5* girls need 3 Lv.100 Bloom and 2 Lv.20 Bloom to evolve.

Don't ask me about 6* girls, I don't have any. :3

6* is 5 lvl 100 dragons to evolve.

It's so much fun to collect that many.