The word for the practise of a woman having many husbands is polyandry.

According to Murdock's World Ethnographic Sample, there are only 4 societies that practise polyandry, all of them in the Himalayan area, but according to this Survey of Non-Classical Polyandry ( Katherine E. Starkweather & Raymond Hames) I've found, there have been others - among Inuit tribes, for example.

It seems the practise was/is more common in societies suffering a scarcety of land and resources, or with a high mortality rate among men. It also seems to coincide with the cultural belief that a child can have more than one father - a concept called partible paternity.

Tibetans have practised fraternal polyandry - the practise of brothers marrying the same woman, and the woman having equal sexual relations (or at least being expected to have) with both brothers. The main reason being to ensure that the land a family owns stays in the ownership of that family - if all brothers marry the same woman, the land does not need to be split up into smaller sections and parcelled out to all children/separate branches of the family tree. In a region with a scarcity of arable land, this mattered; splitting the available land into sections too small to support reasonable agriculture and grazing land was unsustainable.

/r/anthropology is a very good place for this question.

There is a tribal group called the Igbo (Ibo) in Africa that practice a form of polyandry. They are a matrilineal society (trace the family line through the mother, as opposed to how most societies trace the line through the father, patrilineal).

There's a famous minority group in Southern China that often calls itself matrilineal and matriarchal. They are known as the Mosuo. The women in Mosuo society make the rules, do the work, and choose their partners.

It looks like PBS Frontline even had a documentary about them.

The Mosuo don't have a written language, so there's a lot of misunderstanding about their culture. I've only seen Mosuo people once in 2009 in China, so I don't want to pretend that I know much about them. Here's a link to the Lugu Lake Mosuo Cultural Development Association.

Hope you find these links informative!

Related question: In the Bhagavad Gita, Draupadi marries the five Pandava brothers. Was this ever a real thing in India, or just a thematic element of epic poetry?