He decided to design an overnight mail delivery service. Smith did just that and turned his design into a class project. His business professor gave him a C. What is the meaning of the red parts?
"He did just that" just means that he acted upon his thought; in his head, he dreamed of an overnight delivery service and he subsequently put that dream down onto paper and described the detailed operations of such a business.
"Business professor" is the teacher (actually, a college professor) at Yale University who taught this particular class, which was some sort of business management class, and to whom Fred Smith had to submit his written work for grading.