It means that you can tell she is experienced, or has had some interesting experiences, from the way that she speaks/laughs. She has grown older and wiser and this is demonstrated in certain ways, including the way she speaks/laughs (or the things that she speaks about or laughs at).

It means that she has had experiences that changed her and you can feel that in the way she speaks and even laughs. During our lifetime there are things that happen that change us and make us grow up. The narrator wants the reader to know that the woman was less mature before, less aware of things around her or less aware of the true nature of the things around her. Now she has become more mature and this shows in her tone of voice. She laughs the laugh of experience(s).