Polygamy refers to the practice of having more than one spouse. It is broader than polygyny, which refers to situations where one man has multiple wives, and polyandry, which refers to one woman with multiple husbands.
It is widely assumed that polygamy denotes specifically the marriage of one man to multiple women. This is probably because polygyny is more common (or more newsworthy, at least) than polyandry. In current news writing, polygamy mostly appears in reference to North American religious sects that in fact only practice polygyny—for example:
In 1890 the church banned the polygamy for which it used to be notorious. [The Economist]
It was during this period that polygamy was slowly being phased out under pressure from state legislators. [Guardian]
This extensive use of polygamy, which is technically correct, in place of polygyny, which would be more precise, has perhaps muddied the former’s meaning in some people’s minds. For example, these writers seem to think polygamy is the opposite of polyandry:
Polyandry and polygamy, religiously authorized or mandatory, have not survived as legal institutions in the West. [NY Times]
The former Pennsylvania Senator … suggested other “consensual acts,” presumably, polygamy and polyandry, for example, were comparable to same-gender sex. [The New Civil Rights Movement]