Ekapatnivrata is a Sanskrit word. 'Eka' means one, and 'Patni' means wife and ' Vrata' means vow. The word is quite self-explanatory and means a person who has vowed to have only one wife.
This is one of the virtues quoted of Lord Rama in the Hindu epic Ramayana. He remains faithful to his wife Sita, throughout the story. An incident exemplifying this- a demonic witch Shūrpanaķha in guise of a beautiful woman tries to seduce Sri Rama, only to be rejected with Sri Rãma humbly quoting 'he belongs to and can only belong to his wife sīta.'
It provides for a social stability in terms of ideal personal relationships. And Lord rama being an ideal Purush(man) often hailed as a Maryãda-purushottam meaning a dignified(maryãda- dignity) person, best(uttam-best) of men(Purush-man)