In this phrase, "about" means "more or less". It's approximately correct, or right enough to be accepted as correct. Here's your corrected sentence (remember to keep tenses consistent): "When I was describing some social issues in China, he said that sounded about right."

"Sounds about right" can be used when the person is mostly sure of something, but could be wrong. I'm not sure why we add "about", but the meaning is virtually the same. Adding "about" could indicate a little bit of uncertainty over "sounds right". (answer by Mat マット)