Something luxe is very fancy and expensive. If you're used to camping or staying on a friend's couch when you travel, a few nights at a luxe hotel will seem extravagant.
Just like the related words deluxe and luxurious, the adjective luxe is rooted in the Latin word luxuria, "excess or extravagance," and carries the sense of something as lavish and opulent as it could possibly be. Your luxe hotel room might come with pillowy soft, luxe bedding and luxe food like champagne and caviar.