It seems to me it's a not very remote past (something done earlier on the same day as the present action, for instance). That's why I've opted for "have done".
"spiega" is present, so Goncin is right matching it with present perfect. The past perfect would have fitted if the sentence had started with "spiegò",
But the rest of the sentence has to be changed from "in order to them to understand it better" into "in order to make them understand (it) better"