Her name indicates that she was from Cairhien, given that her surname ends with the common Cairhienin ending -dred.
Cerilla was a moderately strong Amyrlin. She negotiated the White Tower's way out of the situations in which her predecessor had enmeshed it. Her strength and influence came in large part from her ability to do that. In most other ways the Hall ran the White Tower and the Aes Sedai.
Despite Cerilla's interest and passion laying in the outside world, the Tower influence over the continent began to decline once more during her reign.