息子をよろしく(お願いします)
Please take care of my son. (From parent to their son's teacher/doctor, for instance)
ご家族によろしく(お伝えください)
Please remember me to all your family.
よろしく is the adverbial form of an adjective よろしい, meaning good, appropriate, suitable or like that. The words following よろしく is omitted, as in the examples above.