What is the Difference Between 讲解 and 解释? I've seen both of them used as "to explain" or "to interpret", but I am not sure if there are differences in connotation or anything else?
Both can function as noun or verb. The basic difference is that 讲解 is "oral explanation", or "to explain orally", whereas 解释 simply means "explanation" or "to explain", and can be oral or written. 

老師在課堂上講解得很清楚。 “The teacher explained (it) very clearly in class." (orally)

老師在課堂上解釋得很清楚。 “The teacher explained (it) very clearly in class." (presumably orally, but not spelt out)

課本第十頁解釋得很清楚。 ”Page 10 in the text book explains (it) very clearly."