I would say there is no exact translation, the closest are:
расслабленный (of a state, mood) - relaxed (literally: loosened - as if being a tie)
расслабляющий (music) - relaxing
непринуждённый (of a person, conversation, situation, style, clothing) - free, at ease (literally: not forced)
спокойный (about anything) - calm
There is also a slang word "ненапряжный" which seems to be the equivalent of "laid-back".