白-white 头-head 白头 indicates white hair 偕-(archaism) together 老-old 偕老 indicates ”become old together“ 白头偕老 means ”live to ripe old age in conjugal bliss“.——from Lingoes

You make a mistake.it means a boy and a girl will stay together forever.

白：白色。white。 头：头发。hair。 白头：头发白。the haire get white.（In China we use white to describe the old people's hair.) 偕：共同，在一起。in the company of ; together with. 老：till get old 白头偕老：reach old age together -- said of a couple; be a faithful old hoary-headed couple; live to a ripe old age in conjugal bliss; live together until old age; remain a devoted couple to the end of their lives; stick to each other till the hair turns grey

白, the color: white. (In English they say "grey hair" sometimes to describe the color of old men's hair. ) 頭, head, hair here. 偕, together 老, old, to get old. See, a wide-abused romantic promise.

祝天下有情人终成眷属！ 我愿执子之手，与子偕老。Yes,i do.Oh,i am so bad.but it's good words.