The union of two men as brothers, lovers, best friends, etc.
The word is not a portmanteau of fraternity and matrimony but coined from Latin frater "brother" and -monia "state or condition of being" on the pattern of matrimony from Latin mater "mother" and -monia.
The etymology suits platonic blood brotherhoods, best friendships, etc. as well as romantic unions (since such unions between men lack a potential mother).
Achilles and Patroclus' holy fratrimony is narrated in the epic The Iliad.
The sermon for the men's fratrimony was based on the fourth chapter of Ecclesiastes.