To CLEAR THE AIR means to somehow resolve a difficult situation between people. It is especially used for talking openly about problems, or being patient and waiting for bad feelings to lessen.

For Example:

“Sharon’s been ignoring me all week because of what I said to her, but we finally talked this morning and it really helped to clear the air.”

After a long and stressful few weeks, the team realized they needed to work together and have agreed on a plan of action. Needless to say, this has cleared the air and everyone feels much more positive.