As you may know by now, she is the transgender--though not, as some have reported, the first such person elected to public office in India. Two other trans mayors were elected before Madhu but court rulings removed them on the grounds that their positions were "reserved for women".
That brings me to a greater part of the significance of Madhu's election: Just nine months ago, India's Supreme Court ruled that transgenders could be legally recognized as a "third gender" or "gender neutral". Before that, "hijras" were outside the margins of South Asian societies, sometimes regarded as even lowlier than cisgender members of the lowest castes.
As a result, they were subject to extortion and all sorts of violence, even (and, some would say, especially) from the police and public officials. Also, hijras had few employment opportunities. So, they often were sex workers or did other kinds of illegal work which, of course, put them in even lower public esteem. On the other hand, they were often asked to perform at public and sacred ceremonies such as weddings because tradition holds that they are devotees, or even descendants, of the goddess Bahuchara Mata, worshipped by Pavaiyaa or the South Indian goddess Renuka.
While the hijras were never a highly esteemed class, they had somewhat more status than they now have. Experts often attribute the hijras' loss of what little prestige they had to the influence of Western notions about sex, gender and morality.
Ironically, the first ripples in what could become a sea-change in the lives of people like Madhu may also be coming from Western influence. Some argue that "transgender" is a Western concept. Whatever it is, its current iteration is certainly different from ideas about hijra. Traditionally, hijra were said to have deformed, or simply different, genitalia. While that is no longer the (or a) working definition in all hijra communities, some still undergo a ceremonial deformation or removal of the testicles and scrotum.
The old way of defining hijra is probably the reason why the term has often been translated into Western languages as "eunuch" or "hermaphrodite". That makes sense when you realize that, until recently, nearly all definitions of gender identity had to do with whatever was or wasn't between a person's legs. (Why do you think they called it "sex"?) Now, with about eight decades' worth of gender-reassignment ("sex change") surgeries having been performed, and changes in traditional gender role, definitions of "female" and "male" have more to do with psychology (or, sometimes, spiritual terms). That, of course, is one reason why many trans people choose not to have the surgeries in spite of the fact that the state of male-to-female work has improved markedly, and why people like me see our surgeries as "the icing on the cake" rather than the very thing that defines us as being in the gender in which we live.
But most of us--I include myself--still check the "F" or "M" box. I did what I did in order to live as a woman, the way I see myself, although I also understand that I came to live by my identity as a woman in a way very different from the way most other women do. It is for that reason that I fully support anyone who decides to live outside of the "gender binary", as Pauline Park calls it.
And, it seems that India has made that a legal option. So, perhaps, the subcontinent has not merely been influenced by current Western notions about gender and sexuality--it has gone beyond them. It will be very interesting to see how that affects the lives of trans people, and everyone else, in India--and whether other countries decide to follow its example. Perhaps mayors of genders we can't even define--or outside of the notion of gender altogether--will be elected. How would that change politics, and life?