Something which appears out of or comes out of thin air arrives unexpectedly or seems to materialise from nothing. This is a popular idiom used more often in informal contexts.

1. Liam asked me to invest £20,000 into his business to help keep it afloat. He must think I can conjure money out of thin air!
2. You have to work hard to create opportunities for yourself. You can't just expect them to appear out of thin air.
3. I really don't think Jane put any effort or planning into coming up with that idea. She seemed to just pluck it out of thin air.

1. The man seemed to come from the shadows as if appearing from thin air.
2. The magician performed an incredible trick where he pulled a playing card out of thin air.