I made him understand the concealed meaning of the sentence.
Can I rephrase the sentence without the word 'make'?
"I spelled out the concealed meaning for him"
"I spelled it out for him"
to explain something in a very clear way with details:
The government has so far refused to spell out its plans/policies.
informal What do you mean you don't understand - do I have to spell it out for you?
This phrasal verb is commonly used in informal contexts. It specifically addresses your use case of concealed meaning most of the time it's used.
I taught him the concealed meaning of his sentence.
'Taught' suggests more than for example 'explained' or 'pointed out'. 'Taught' suggests the information has been not only received but understood. After all, if there is no learning going on, there is no teaching going on either -- only attempted teaching.
"I enlightened him on the concealed meaning of the word. A synonym given by this source is "to instruct."