Which one is correct? "Explain me" or "Explain to me"?

Which of the following expressions is correct?

Explain me.

Explain to me.

I know that explain it to me is correct, but I want to know which one of the above is valid.

Explain is normally monotransitive in that it typically occurs only with a single direct object, as in ‘I will now explain the mysteries of the universe.’ If we want to reveal who is to be the beneficiary of such wisdom, we must use a preposition phrase and say ‘I will now explain the mysteries of the universe to the assembled throng.’

It follows that the sentence ‘Explain me’ can, in most contexts, only, and most improbably, be an invitation to elaborate on the speaker’s personality in such a way that we will all better understand the speaker's behaviour. ‘Explain to me’, on the other hand, requires a direct object, such as ‘the mysteries of the universe’, to make any sense. There may be some circumstances in which to is omitted, making the pronoun an indirect object, but in contemporary English they are not numerous.

Dear Dr. Freud,

I am having an identity crisis. I no longer understand myself.
I would like to book an appointment with you so that you can explain me to myself.

yours sincerely,
Mr. Smith

Or

Child: do you like my picture?
Parent: It's lovely! Why don't you explain to me what it is?

It appears to depend on the context.

Explain is a transitive verb (it take an object), so you can say "please explain cartography", or "explain apples", etc. It is also a ditransitive* verb, so it can take two objects,

e.g.

explain to the tree what it is

object 1: the tree
object 2: it

explain to him how to do it

object 1: him
object 2: it

Which is just like how you might use show

show [to] me what it is

vs.

show what it is to me

*Thanks to FumbleFingers for the info

"Explain me" in the context you probably are thinking of, would be pidgin English.

The only way it would make sense if it meant that "me" was the thing you want explained. "Explain mathematics", "Explain cars", "Explain me".

"Explain to me" is perfectly fine, either as part of a sentence...

Explain to me why you did that.

... or with the rest of the sentence provided by context.

I don't understand why you did that. Explain to me.

The meaning of "correct" here is a bit slippery. People usually say explain to me...

I don't think the word "to" is either grammatically or logically necessary - we don't normally bother with it in give me, show me, lend me for example. But given we normally do include the preposition in explain to me, OP should be aware that some people will think he's ill-educated if he doesn't follow the majority usage.

EDIT: Being in "chart mode" here, I'll just include a related construction give it [to] me, where this chart clearly shows how usage has shifted over the past couple of centuries to favour including the preposition...

As with explain, the primary argument for including "to" is simply that this is what most other people do. And the primary argument against doing it is that other people tend to think if you don't copy the most common usage, you're not a competent speaker.