(Click the character infographic to download.)
Fanny is basically the female version of Henry Foster; an example of what a normal woman is like in the brave new world. Since we as readers are interested in the exceptions—Bernard, Helmholtz, Lenina—we have to know what the typical characters are like in order to compare them. Whereas Lenina tests the waters of monogamy, Fanny is resolutely promiscuous. She dutifully takes her pills and pregnancy-surrogates, is materialistic, and generally follows the rules.
As far as the novel goes, Fanny is really more of a narrative device than an important character. Her presence gives Lenina someone to talk to, which means we get to hear 1) Lenina's thoughts, and 2) the way those thoughts might clash with the general opinion of World State citizens. Clever, no?