Both can be translated as "young" in English. However, 어리다 is usually used for from infants to teens, and 젊다 is more likely for from youth to young grown-ups. You could also use 젊다 even if the people aren't very young but you are older. I hope it helps, -Ahtti

if your age is under 20(there is any absolute standard, though), you can be..어려요. But you will still young(젊어요) until you are around 30~35, maybe? But these also can be used relatively, like ~보다 ~살 어리다. (나는 Tom보다 2살 어리다. I am 2 years younger than Tom) or ~보다 젊다, 어리다.(나는 Tom보다 어리다.or 나는 Tom보다 젊다 Both are okay = I am younger than Tom)