1. Literally, to unroll a large red rug or carpet for a very distinguished or important guest to walk on. The theater put out the red carpet for the duke, who was attending the opening night of the play that evening.

2. By extension, to welcome someone with a great or elaborate display of hospitality, ceremony, or fanfare. Since Jake was their only child, Robert and Sarah always put out the red carpet for him whenever he returned home from college. We're just popping by for a cup of tea and a quick catch-up, no need to put out the red carpet!