Open-air means it happens outside, with the sky above you, not in a hall. An open-air concert, an open-air market, an open-air pool, an open-air film in summer. People still often write the little line in the middle. It feels a bit more like a named kind of place than just saying outdoor: “open-air theatre” is a type of theatre. If it rains, the open-air plan is in trouble — that is the whole point of the word. In cities, shops also use it to sell a holiday feeling, even when you are only in a yard with lights. You can say the concert is in the open air, with a space and no little line; the hyphenated form is the one that sits in front of a noun.