I think you need the first one. To me, the second one can have a completely different meaning, where "to me" goes with "means": you might be asking somebody (say, John) to explain to somebody else (say, Mary) your understanding of a sentence. However, I wouldn't see any ambiguity if instead of "what the sentence means" you had another object (as, for instance, in "Please explain the task to the students").
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User_garyPlease explain to me what the sentence means.They are both grammatically correct.
Please explain what the sentence means to me.
Which one is correct?