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).