explanation for something = a reason something occurred explanation of something = a description of something Explanation for your bad grades = "I didn't get much sleep", "I didn't study", "the teacher is very intimidating" Explanation of your bad grades = "I got a D in math", "I failed my oral exam", "I received an incomplete on my homework assignments"

"There can be no explanation for this bad behaviour" "Can you give me an explanation of the different uses of this word?" In the first case, there is no explanation why something happened. In the second case, "of" is used normally. If I think of a better way to explain myself, I'll post a comment later, but I hope this gives you a start.