In order for Kagura to awaken, she must consume enough Red Orbs, allowing her to advance in her stages. According to Dōgen, Red Orbs infused with shinobi blood are more potent, making the Red Orbs of the ten Yōma Generals very effective at awakening Kagura.
They are apparently somewhat fragile, as Murasame manages to destroy one by accidentally stepping on it.
In the Waist-Deep DLC campaign, it was shown that if Kagura coughs up her Red Orbs she can revert to her child form, and that if a regular human consumes a Red Orb they will transform into a "chibi" form until they cough up the orb.
When playing as Kagura in Senran Kagura: Estival Versus, her intro shows her in her child form and she consumes a single Red Orb and skips her teenage form and goes straight to her adult form.
They take the form of a small, red, opaque marble-like sphere bearing the mark of the Goshin Clan.