1. physically hang something wet to dry off
hung out to dry on the clothesline
To 'hang' something means to suspend something from above with a lower part dangling free. When you 'hang something out to dry' or 'leave something out to dry' it usually refers to using a clothesline or a washing-line to dry fabrics or items of clothing outside.
2. left to take the blame/punishment; leave someone in need
left hung out to dry
When you 'hang someone out to dry' it means to abandon them when they need your help or to leave them alone to face a situation which is unpleasant. It can also mean to allow someone to face punishment or criticism unfairly without stepping in to help or defend them. This is an idiomatic phrase similar in meaning to 'throw someone to the wolves' or 'to leave someone high and dry'.