A lady who knows what time it is

Posted by Kashima on September 02, 2004

I'm now listening to a song "Sadder-But-Wiser Girl" from the famous musical "Music Man".

Professor Hill sings to his friend that he prefers sadder-but-wiser woman to innocent, eager, pure, baby-doll girls, because the latter type of girls will merely take away his independence.

The lyrics are:

I spark, I fizz for the lady lady who knows what time it is,
I cheer, I rave for the virtue I'm too late to save,
The sadder-but-wiser girl for me.

Would someone help me with the meaning of the phrase
"a lady who knows what time it is", please?