I am learning English, but I am not familiar with idioms. Could somebody explain me in plain English what does it mean "I will need to come back to you on this request."
I usually hear this as "I will have to get back to you on this" in AmE, although "come back to you" is also used. It means, I will have to do some investigation or work before I can fulfill your request or answer your question. For example,
"Can you tell me the date of my last payment?"
"Let me check my files and come back to you on that. Is there anything else I can help you with?"
In my experience, "get back to you" is more common than "come back to you", but the context suggests it's the same meaning.
It means "I cannot answer you right now, but I will answer you later."
Maybe the speaker doesn't know the answer yet, and so plans to go research it, and then tell you the answer based on their research.
Maybe the speaker does know the answer, but doesn't have time to deliver the answer properly right now. (Because the answer is long and complex, or requires a diagram, or something.)
Maybe the speaker doesn't know if they have permission to answer you - the information may be confidential, so they need to go find out if they're allowed to disclose it to you.