To make no bones about something is to say clearly what you think or feel about it. Of course, this could leave the listener offended or embarrassed. And in some cases, being too frank can cause some embarrassment for the speaker as well.

The editor made no bones about his dissatisfaction with the quality of the articles I submitted. (Of course, when he frankly says that he is not happy with my articles, it will embarrass me, but he doesn’t care.)

She made no bones about her desire to end their relationship.

She made no bones about her addiction to drugs.

The boy hadn’t done his homework and made no bones about it. (= The boy candidly admitted that he hadn’t done his homework.)

The actress was having an affair with a rich industrialist and made no bones about it. (= The actress didn’t try to hide their relationship. In fact, she was very vocal about it.)

According to scholars, this idiom has been in use since the 1500s. Some people believe that it is associated with soup. If there were no bones in the soup, people could swallow it easily without having to worry about chocking. And when you make no bones about something, people can swallow or believe what you say because you are saying it frankly.