This is the 5113th most frequent Korean word.
내민
"내민" means "extended" or "held out."
The word "내민다" is derived from "내밀다" which means "to reach out" or "to extend." Here, it describes the action of presenting a gift.
그녀는 나에게 작은 선물을 내민다.
She hands me a small gift.
In this sentence, "내밀고 있었다" describes the action of extending a branch, emphasizing an outward gesture.
작은 새가 가지를 내밀고 있었다.
A small bird was extending its branch.
"내민" is used here to depict the act of offering assistance or help by literally or figuratively extending a hand.