Cordelia grew up on Beta Colony, and is living there with her mother and brother at the beginning of Shards of Honor
, but later flees to Barrayar
to marry Aral Vorkosigan
In the book Barrayar, she explains that she has been many things in her life: she was a Betan survey captain, and then she was a POW, and then she was a refugee, and then she was a wife, and then she was a mother. Later she reminisces about this to her son Miles's first love Elena Bothari, who is inspired to feel that like Cordelia she has had enough of being a soldier and would like to do something else with her life.
She is a very wise and caring person who listens to and helps everyone she knows, a trait Miles seems to have inherited from her (he thinks of it as being a carrier of forward momentum).