Usually, the brackets include a part of the sentence that wasn't said but the interviewer believes the speaker meant or was implied.

In cases like this, maybe the speaker was speaking quickly (and, so, didn't say the words during the interview) or were dropping implied parts is the sentence (like we all sometimes do when speaking casually; like if I say, "Quick thinking," to someone. It's implied that I was saying, "[That was] quick thinking").

This also gets used often if the interviewee is talking about someone they know personally but we don't so they're usually just using the first name (e.g. "Yeah; me and [General] Howard [Zimmerman] go way back").