"Explain" means that you're trying to help the person understand what something is, or how it works. "Interpret" means that you translate what someone in trying to convey. "Paraphrase" means that you're re-using someone's idea, or sentence, but with your own words. I hope that's clear :) Tell me if you need any precision and good luck with your learning!

If there is something that you don't understand, somebody needs to explain it, i.e. to make it understandable. You can try to explain something by paraphrasing, i.e. by using other words to say the same thing. However, a dream, a novel, a painting or a piece of music - sometimes even statistics or graphs ;) - can not really be explained, but they can be interpreted, often in lots of different ways, i.e. you can say what you see in them. Hope that helps.

Explain - a more general way of conveying more clarity and meaning in an idea, thought, or thing. Interpret - usually an attempt to translate or find meaning in abstractions--most commonly in language and stories into one's meaningful words or logic. Paraphrase - can be synonymous to explain something in a different resolution but with an intent to maintain the semantic logic and structure in phrases or sentences.