The verb "배웠습니다" means "studied" or "learned". It is the polite Past form of "배우다".
Here's the sentence broken down for you:
저는 = I
한국 = Korea
이화대 = Ihwa University
에서 = at
마케팅 디자인 = Marketing Design
을 = (particle indicating the direct object of a verb)
배웠습니다 = studied
Here's another example of "배웠다" in action:
It's helpful to use "My Vocab" to save words to your personal word list (select the word and click the ABC icon). I hope that helps!