1. to flatten or even something by smoothing or pressing.
> Wally smoothed the bedspread out.
> Wally finished making the bed by smoothing out the spread.

2. to polish and refine something.
> The editor smoothed John's style out.

3. and smooth something over to reduce the intensity of an argument or a misunderstanding; to try to make people feel better about something disagreeable that has happened. ( on Q.)
> Mary and John had a terrible argument, and they are both trying to smooth it over.
> Let's get everyone together and try to smooth things out. We can't keep on arguing with one another.