It describes something or someone that is:
* Characteristic of a matron: meaning a mature woman, especially one who is married and has a family.
* Having the appearance or qualities of a matron: This could include being dignified, respectable, and perhaps a bit stately.
For example:
* "She had a matronly air about her, with her elegant dress and pearl necklace."
* "The matronly figure of the headmistress commanded respect from all the students."