Does this mean that there is no interest at all accrued on an unsubsidized loan? Or does that mean that the interest will be accrued later? See I understand that the interest on a subsidized loan accrues after your are finished with school or you are enrolled less than half time, but I do not understand about the interest on unsubsidized loans.

Subsidized loans mean that the government subsidizes (essentially, pays) your interest while you are in school. Unsubsidized loans, on the other hand, mean that interest accrues immediately from the time they are disbursed, even when you are in school. Generally, you should take subsidized loans before unsubsidized as they are cheaper in the long run.