Jane Doe is an agent of the CSA.
That acronym stands for the Central Security Agency and it represents a federal government intelligence organization that handles a wide assortment of situations from major crimes like substantial art theft and tracking down of murderers to counter-espionage. While each of the missions we see being handled appear to be domestic, there is nothing to indicate that foreign activity is not also handle by this group. What we see, though, is those cases happening in the Los Angeles area.
That is where Cathy Davis lives and works. She is the wife of Jack Davis (a residential home builder, I believe) and the proud mother of two, Susan around 16 and Zack who is about 12. Davis also has a day job she enjoys a great deal and at which she shows over and over how good she is, designing games and puzzles for kids.
It is when she is approached at a supermarket by Frank Darnell, likely Special Agent in Charge of the L.A. branch of the Agency that we learn that the two had worked together for many years quite a few years before. Davis and Darnell had been partners and had amassed an impressive list of successes before Davis decided she wanted a home life more than she wanted to be an operative.
Since Davis did not want her renewed involvement with the CSA to become known to, well, anyone, it was agreed that when she appeared at the headquarters or worked anywhere in a semi-official basis, she would carry an id/badge that clearly identified her as Jane Doe. While that would hardly be considered real, it would still be enough to not let others know who she really was.
It had been agreed when she was asked to help that first time that it was strictly a one-off situation. Obviously by the fact that we have several recorded adventures of her providing much needed help, one time turned into more than a few.
Initially she kept her return to duty, if just temporary, as secret from her husband but after a while she found that unacceptable so confided in him. As far as I can tell, the teenagers remained unaware.
In one episode we discover that being a government agent runs in the family when another former CSA agent is pulled, Davis's mother, Polly.