After getting hitched to Nathan, Rukmani enters the marital home, a humble mud hut whose doorway is adorned with a garland of mango leaves. According to local tradition, this is intended to symbolize happiness and good fortune.
The irony here, of course, is that Rukmani feels anything but happy or fortunate to have married Nathan. Whereas her three sisters have all been married off to well-to-do husbands, Ruku has been forced to marry beneath her social status. Even so, Ruku accepts her lot without demure. So long as she's married to Nathan, she's determined to make the best of a bad situation. In that sense, the garland of mango leaves represents her abiding hope that her marriage will work out alright in the end. For at this precise moment in time, hope is really all that Ruku has.