In this context "well rounded" means "versatile" or "many-sided", that is having good (enough) knowledge of various subjects.
A "well grounded" individual has a working knowledge of a certain field.
All in all, the school tries to educate their students so that they have a broad enough knowledge of various subjects in their field, while at the same time the knowledge of those subjects is good enough to be used in practice.
If that didn't make it clear enough, just say so and I (or someone else, I'm sure) will elaborate some more.
Student or Learner