The Handmaid's Tale presents a dystopian near future with several sexist and classist new terms and roles to learn. What is a Martha in The Handmaid's Tale? Early on in the series, Serena Joy scoffs that Offred is "not a Martha," but this is not a name — it's a title.
Marthas are essentially maids, or housekeepers. They do cooking and chores for wealthy families. They nanny the children. What separates them from wives is their low social status. What separates them from the handmaids is their infertility.
In the first episode, the Martha that Offred lives with is not particularly nice to her — though the oppressive regime they both live under has done plenty of heavy lifting so as to ensure that women resent and do not trust one another. Her name is Rita. That's another difference between them and the handmaids. Marthas get to keep their names. And, they don't seem to want to help one another, or even talk to one another.
Just like the role of the handmaids is inspired by the biblical tale of Jacob, Rachel, and Leah, much to my own biased chagrin, the figure Martha in the Bible was a hostess consumed and happily obsessed with chores — but also heavily implied to be a homeowner. That's interesting to me. It suggests that housekeepers end up running the house in more ways than one, possibly due to their wealth of information. Marthas have a different kind of power and some different kinds of freedom in The Handmaid's Tale, which may end up coming into play later.