O que significa Ben had found out from Philip that she was the senior class’s runaway valedictorian with Philip himself an earnest but distant second. ?

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When students graduate from university, the graduating student who ranks the highest will speak to the graduates at the ceremony. This is the valedictorian.

In your sentence, the girl (she) was the highest ranked. Philip was in second. Her score was much higher than Philip's score. When people are competing and there is a big gap between competitors (usually between first and second), you can describe it as "runaway" because it is like second place cannot catch first place.

Philip tried very hard without cheating. He competed "earnestly".

Another way to say this is "Ben had found out from Philip that she was the class's valedictorian. Philip was ranked second. Although Philip tried very hard, there was a big gap between their rankings."