What does the phrase "woman who does" mean?

Yes, it is a woman who does household chores for remuneration. She does not live as a member of the household.

The OED's entry for do, under Phrasal Verbs, has an entry to do for —, whose definition 1b is:

colloq. To attend to; esp. to perform household tasks for, esp. as an employee.

They give (among others) a 1997 citation from the Daily Telegraph:

Mrs Simmons has ‘done for’ Mrs Lynton-Smith for 24 years.

In context, it usually refers to light cleaning and housekeeping tasks. As chasly says, it doesn't seem to include live-in servants.

A woman who does might have been called, in earlier times, a charwoman or daily woman.

We had a woman that does when I was a child, it's the old language for a cleaner who came daily to clean the house, made the beds and did the washing for people who could afford to pay. We had one because my mother had never done any housework as her family always had live in servants so when we moved to a smaller house she needed the help especially as my grandmother lived with us.