아프지 마요 literally means "Don't get sick". * 아프다(a) = be sick; feel pain. * A/V-지 않다, -지 못하다, and -지 말다 all negate A/V with different connotations. -지 is a fixed negator conjugation form. - A/V-지 않다 = don't V / isn't A. 나는 아프지 않아 = I'm not sick. 나쁘지 않다 = It's not bad. - A/V-지 말다 = won't V / won't be A (implies an intention, so it's used in imperatives). 가지 마(요) = Don't go. - A/V-지 못하다 = can't V / can't be A. 가지 못해 = I can't go. 나는 독일어를 하지 못한다 = I can't speak German. So 아프지 마요 is a polite imperative sentence for "Don't get sick", or "Stay healthy". It's not something we say often like a greeting though. 건강하세요 (Keep in health) or 건강하시길 빌어요 (Wish you good health) are more common.

It is similar with 'Take care'.