The characters of Shuffle! have a theme of being named after plants. In this case, her given name, ama (亜麻) refers to Linum usitatissimum, commonly known as flax. Her surname however, shigure (時雨), is a Japanese word that refers to the frequent rains that occur during late Autumn or early Winter in Japan.
In fact, Ama is not a human, but the first artificial life-form by the Yggdrasil project. She wears a cat-eared or tanuki-eared cap in order to hide her ears.
Originally a devil, she was the first volunteer for the project (a joint effort by both the god and devil races). Her reason for joining was that she saw no purpose in her life or future. The project involved enhancing Ama's magical powers to extraordinary levels, thinking that this could give her extraordinary magical powers, include the power to perform resurrections or to prevent aging.
Unfortunately, the experiment proved to be too much for Ama. The experiment went awry and an explosion caused by Ama vaporized the lab. Ama, however, survived the ordeal because she was teleported to the human world, by means unknown even by herself. Here, completely naked and lost, she was rescued by a human, with whom she fell in love. She later gave birth to Asa, and by heredity transferred her magical powers into Asa. Because Asa is born with a human body, her physiology cannot handle the magical powers she receives. Thus, she is often ill and in bed.
The second time, Ama appears while Rin is walking home with Asa. Ama is going to go buy ingredients so that Asa can bake a cake, to which Asa replies that she should have just asked her to pick them up on the walk home. Ama says she doesn't mind though, as she likes to go on walks. Shortly after this, Asa suddenly collapses, scaring both Rin and Ama. Asa claims to be ok, but Ama asks Rin to take Asa home just to be sure.
The third time Ama is present is just before the second H scene with Asa. Ama asks Rin if she's come to see Asa and is disappointed to know that she has to go elsewhere. Basically just setting up the fact that Rin and Asa will be alone in the house together.
The final time Ama appears in the game is when Rin meets her alone in the city. She confirms that she is an artificially made lifeform and explains how that's caused Asa to be weak.
Ama is first introduced in episode two when she meets Rin and Primula. After staring at Primula for a bit, she notices something strange about Primula but does not say anything.
At the end of the series, both the devil and god kings meet Ama when they are walk past her downtown. The two pause for a bit, ponder, then eventually leave, noting that she looks very familiar. Ama turns around as they walk away, takes off her hat, and bows as a thank you to them. The kings knew who Ama was but decided it was best to let her live her own life and note that if they could meet her again, they would apologize as they did something terrible to her.
Ama returns as a secondary character in Really? Really! While still not a pursuable character, she does have multiple CG scenes where she appears nude.