Can you explain this word to me?
Can I rephrase it as
Can you explain me this word?
Consider the following examples -
He gave Mary ten dollars.
He passed Paul the ball.
The verbs - give and pass - are the examples of ditransitive verbs. They take both an indirect object as well as a direct object.
The pattern for ditransitive verb is -
ditransitive verb + Object indirect + Object direct
Consider the following sentences -
I borrowed the money for her.
We can't write the following sentence -
- I borrowed her the money. (INCORRECT)
The verb - borrow - is monotransitive verb and can't be used like the way ditransitive verbs are used.
Though there are some verbs that can be used both as ditransitive verb as well as monotransitive verb. Like give and pass
He gave ten dollars to Mary.
He passed the ball to Paul.
And there are verbs that can only be used as a monotransitive verb, never as a ditransitive verbs. Explain is one such verb.
He explained [something] to me.
He explained to me [something].
- He explained me [something] (INCORRECT)
For further reading regarding this subject, please refer to The Cambridge Grammar of the English Language (2002) page 308, section 8.2
My intuition as a native speaker of American English with a Midwestern upbringing is to simply say no. The verb "to explain" does not license an indirect object, and you need to use a prepositional phrase like "to me" for that sentence to make sense.
Native intuition is often correct, but it rarely counts as a useful answer. The following isn't a comprehensive answer. It's only a rule of thumb. It's meant to be a preliminary guide until you find a better guide.
What does the recipient receive? Give me an answer.
Let's look at my last sentence:
Give me an answer.
That's an imperative sentence. The subject is you, whom I address. The verb is a form of "to give". The indirect object is "me". The direct object is "an answer". If you give me an answer, then simply and literally, I receive an answer.
We can contrast this with your sample sentence. I'll even phrase it in the imperative to make the contrast simpler:
Explain this word to me.
In that sentence, what does "me" receive? Not the word. The explanation. Not the object, but the result of the action.
In my sentence, "me" gets the answer -- the indirect object gains possession or control of the direct object. In your sentence, "me" does not get the word (the direct object) even though "me" gets the benefit of the action (the explanation).
There are exceptions, and you will encounter those exceptions as you learn the language. However, until then, as a rule of thumb, reserve the indirect object construction for times when the indirect object receives the direct object.
Following that rule of thumb, you might use prepositions when you don't need to, but you'll not use a preposition where it isn't warranted.