What Is a Well-rounded Musician?

I think a well rounded musician is someone who has the skills to play whatever they set out to play correctly and expressively. Notice, I said "whatever they set out to play" not can play anything. There are so many styles of music that it is virtually impossible to be good at all of them. Well rounded musicians know what styles they play and how to do them well. They can decipher the notation and have the skills to bring what is on the page to life. They can isolate necessary skills (figure out the rhythm, what notes to play, how loud or soft to play, how to interpret the score, etc). They can do it all independently, but also know how to take direction so as to mesh with a group and/or express someone else's vision. Well rounded is about doing what you do well. The skills will also transfer to styles outside of what you normally do. For example, I normally focus on classical and church music, but I'm currently working on Maple Leaf Rag. I can play it and it's fun to get outside my normal style.