From ODO's definition of Martha:
(in the New Testament) the sister of Lazarus and Mary and friend of Jesus (Luke 10:40).
(as noun a Martha) a woman who keeps herself very busy with domestic affairs.
Wikipedia's page has more information on Martha (of Bethany). It includes an excerpt from The Catholic Encylopaedia:
The familiar intercourse between the Saviour of the world and the humble family which St. Luke depicts is dwelt on by St. John when he tells us that "Jesus loved Martha, and her sister Mary, and Lazarus" (11:5). Again the picture of Martha's anxiety (John 11:20-21, 39) accords with the picture of her who was "busy about much serving" (Luke 10:40); so also in John 12:2: "They made him a supper there: and Martha served."
I suspect that all these mentions of Martha being busy serving is the source of meaning.
Etymonline's entry confirms this:
fem. proper name, from Aramaic Maretha, lit. "lady, mistress," fem. of mar, mara "lord, master." As the type name of one concerned with domestic affairs, it is from Luke x:40, 41.