Medama hold memories of children from old Redo; a Ratatan's gift turns Chorus into Cobun. In other words, every Cobun marching behind your leader started as a Chorus that received one of these relics.
What are Medama in Ratatan?
Medama are relics that house the memories of the children who lived on planet Redo long ago. The developers' own answer adds a twist: those children are you, the player.
That fits what the ending tells you about the planet. Redo was built by Humans as a place to play, and no Human has come back in a long time. Medama keep the memories of the children who once played there, which is why the Ratatan ending keeps returning to the question of who can give the planet its sense of wonder now.
Where do Medama come from?
The first Medama you see goes into your own Ratatan. At the very start, in a place called Nowhere, Crow wakes your Ratatan by putting a Medama into it. From there you set out with Fortrun toward the Goddess.
That makes the relic the starting point of the whole journey, not just of the Cobun. Crow and the singing ship that travel with you are covered on the Ratatan Fortrun page.
How do Medama turn Chorus into Cobun?
When a Ratatan gifts a Medama to a Chorus, the Chorus becomes a Cobun. The new Cobun takes on the appearance and traits of the Ratatan who gave it, and it acts through music and song.
You can see the resemblance in the official art: the small one-eyed Cobun copy the ears, wings and spikes of the leaders they march behind. That is the gift at work. A Cobun is a Chorus wearing its master's look.
Music is the other half. Because Cobun answer to song, you lead them with rhythm commands instead of controlling each one. The Ratatan how to play guide covers those commands, from Fall In to Attack.
Why do Medama matter in the story?
Medama tie the Cobun to the planet's past. Each one carries memories of the children who once played on Redo, and each gift turns a Chorus into a companion who keeps those memories moving.
That is the idea the ending builds on. When Crow suggests working with the Cobun instead of bringing Humans back, he is betting on the creatures the Medama made. If you have already beaten the final boss, read the Ratatan ending next to see how the Goddess answers.