Fetching details from the dictionary...
to draw (water); to scoop up; to dip up; to pump out
to understand (someone's feelings, etc.); to grasp; to surmise; to take into consideration
彼の気持ちを汲み取った。
I read between the lines of his feelings.
彼は客の本音を汲み取っている。
He is picking up on what the customers really think.
相手の気持ちを汲み取らないとうまくいかない。
Things won't go well if you can't read the other person's feelings.