I have a question about tenses in English. When would you say, "Someone had heard that something happened," instead of "Someone heard that something had happened"? I'd really appreciate it if anyone could give me a specific example.

They are both grammatically correct it is just that the former is using perfact past. As sited from Cambridge Grammar of the English Language " The preterite perfect [i. e. the past perfect] locates the writing anterior to an intermediate time which is anterior to the time of speaking - it is doubly anterior (140)."