Literally, this means "until black hair becomes like a leek root." A leek root is white and stringy, so Koreans use it as a poetic image for white/gray hair. The phrase means "until your hair turns white with age" — in other words, "for the rest of your lives, growing old together."

It's one of the most common phrases used at Korean weddings, similar to how English speakers might say "until death do us part" or "growing old together." You'll often hear it in a wedding officiant's speech, or see it in storybook endings like fairy tales.

Example:

왕자와 공주는 검은 머리 파뿌리 되도록 오래오래 행복하게 살았다.

"The prince and princess lived happily ever after, growing old together until their hair turned white."

So if a Korean friend says this at your wedding or uses it to describe a couple, they're wishing you a long, happy marriage that lasts a lifetime.