Very simple. 

"Well-rounded tone" in such cases means that the instrument has a vast range of possible tonal expressions.  It may be squawky, squeaky, shrieky, whistling, buzzing, rattling, nasal, muffled or even flatulent.  Particularly well-rounded instruments may be able to exhibit more than one of those qualities at once.

If you are particularly fortunate, they may sometimes also be "automatically microtonal".  Such rare instruments can be identified quite easily.  Tune any string and bow the open note for a minute or two.  Automatically microtonal instruments will slowly shift through every frequency between what you tuned it to and a pitch several notes below that one with no further effort on your part, as if by magic!