take (one's) point
To understand and/or come to agree with a particular point someone is trying to make. A: "The early flight might be cheaper, but we won't enjoy our first day there because we'll be so tired!" B: "OK, I take your point. Let's book the later one instead." But Bob, if we don't secure the investment by Friday, we stand to lose everything the other investors had put in so far. Do you take my point?
take someone's point
Understand what someone is saying, concede the truth of what someone said, as in Am I taking your point correctly when you say you disagree but do not object? [Late 1800s]
take someone's point
accept the validity of someone's idea or argument. chiefly British