It means "in a way that is relatable". In other words, although the fancy bags and designer clothes give her a magnificent and imperious air, they don't hide the fact that she's an elderly lady. She's relatable because physically she looks like any other elderly woman, so when you look at her face it reminds you of an elderly woman you know or knew, especially one who pushes or pushed the boundaries when dressing themselves. The author gives the example of an aunt, but it could equally be a friend, an acquaintance, a grandmother or the crazy lady who lives across town.
It's not common in everyday speech, but it does exist and it's good to understand it.