When we say "explain X", then X is the mystery. If there's a listener, then we say "explain X to (somebody)".
We can't use the "[verb] [indirect object] [direct object]" pattern simply because the verb "explain" doesn't work like that. There are a few other verbs which cannot take this pattern, although the common learner mistake is to assume this word order is automatic.
On top of that, the English pronoun is the same for both direct (accusative) and indirect (dative) objects. So, a preposition is needed here to show who the listener is.
When a student writes "please explain me...", then to native speakers, "me" is the mystery and it sounds funny that the writer is completely confused by him/herself! :)