Kyouko Kasodani is a yamabiko, a youkai that politely echoes back whatever somebody yells at a mountain. Yamabiko are common youkai that have been found on every mountain since ancient times.
Kyouko's daily schedule starts in the morning with sweeping Myouren Temple. She also chants sutras in the mountains every day. This might be the source of a frightening rumor among humans about hearing a voice chanting sutras in the mountains even when nobody is around.
Youkai die when they are completely forgotten or when their existence is explained by something else, such as a natural phenomenon. Yamabiko are said to have lost their reason for existing and disappeared when the humans in the village claimed that yamabiko were actually just reverberations of sound.
Yamabiko normally only parrot back the words that are spoken, but there are some situations where the echo is slightly different from the original. However, if you yell "What is one plus one?" at the mountain, you will not get an answer. Perhaps yamabiko are not too good with numbers...
Kyouko is more often at Myouren Temple than in the mountains. As usual, she is hard at work sweeping today. Apparently, when she hears Byakuren's sutras, she memorizes all of them and ends up chanting them herself. Of course, she has no idea what they mean, but she seems to have fun doing it anyway, so why not let her enjoy herself?