The phrase, patience is a virtue, means “it is good to be patient,” where patience means “the ability to wait peacefully for what you want—without becoming anxious or angry.”
This meaning of patience is not related to the word a patient, which is “a person under medical care.”
The word virtue has a long history in Western philosophy. Long ago, virtue meant “an ability or power,” and it is still sometimes used this way:
This plant has the virtue of curing headaches.
However, nowadays, virtue usually means “a positive character trait” or “morally correct behavior.”
Virtue gained its modern meaning from Christian philosophy, in which virtues are the opposite of sins (breaking God’s rules). According to Christian tradition, there are seven most important virtues—chastity, temperance, charity, diligence, kindness, patience, and humility—and these are opposed to seven deadly sins: pride, greed, anger, envy, lust, gluttony, and sloth. Neither of these lists comes directly from the Bible, but rather from medieval Christian philosophers.
Patience is a virtue is a common saying, perhaps because people are so commonly impatient.
The saying first appeared in print in the 14th century in the poem Piers Plowman, by William Langland.