(deyim) Talk about a problem to someone so that it doesnt bother you anymore: "I finally talked to my friend from work and was able to get some of my problems off my chest."
(deyim) Told to someone and so not bothering you anymore; not making you feel worried or upset, because you have talked about it. "After Dave told the principal that he had cheated on the test, he was glad because it was off his chest."; "Father felt that Tom wasn't helping enough around the house, so he got it off his chest by giving Tom a list of things to do."