Agamy refers to a social condition wherein marriage, in any form, is not recognized. It is rooted to the Greek city, Agami. In this condition or state, marriage is not a social institution. There are no rules on marriage -- no regulations on how to get married and dissolve marriages. It is not prescribed to people who have sexual or romantic relations.
More About Agamy
Today, marriage is recognized as a legal institution in practically every country worldwide. Agamy exists only in small social groups. These groups are likely to practice polyamory. Within a polyamorous group, marriage is seen as too restrictive. It is bound by too many rules. It is understandable why they would choose to not recognize it as part of their lifestyle.