Concept:The idiom “by and by” means “before long” or “after a short while.”
Explanation:In the sentence, “We shall understand her better by and by,” the phrase “by and by” describes a time that is near, not distant.
It tells us that within a short time, we will gain a better understanding of her.
Option C, “before long,” matches this meaning exactly.
Option B, “much later,” suggests a longer delay, which is not what “by and by” implies.
Options A and D do not relate to the timing expressed in the sentence.
Answer:C. before long.