This is the 4597th most frequent Japanese word.
怖く
"Scary" or "frightening."
In this example, '怖く' modifies the action of crying, indicating the emotional state causing it.
妹が怖く泣き出してしまった。
My younger sister started crying out of fear.
Here, '怖く' is used as an adjective to describe the state of feeling scared or frightened while walking on a dark road.
暗い夜道を歩くのは怖く感じます。
Walking on a dark night road feels scary.
'怖くて' shows causality due to being scared, leading to the inability to open the door.