As I understand it, this phrase when applied to people, usually women, means in general that they require a great deal of attention and time. It can refer to beauty treatments: a high-maintenance woman would spend a lot of money and time on regular manicures, facials, Botox injections perhaps, and so on. I think the phrase can also refer to someone with a personality that demands a lot of attention: her boyfriend has to call her several times a day & spend a lot of money on her, her girlfriends have to spend time listening to her describe every aspect of her daily life and provide lots of sympathy for minor troubles, etc. Not a very flattering phrase!
[not a teacher]