to give ear: to listen closely and attentively to what someone says
This word does not mean simply to notice a sound. It is built from the word for ear, and it pictures someone bending the ear toward a speaker to take in every word. So it always carries the idea of deliberate, focused attention rather than passive hearing.
Because of that focus, it lives almost entirely in poetry, and it is a favorite word for calling an audience to attention. A psalmist, a prophet, or a wise teacher opens with it to demand that people stop and truly take in what follows. It is constantly paired with the ordinary word for hearing, the two reinforcing each other: hear me, and give ear to my words.
The same word also describes the listening that people most long for from God. When someone in distress begs God to give ear to a prayer, the plea is not that God would merely notice the sound but that he would attend to it and act. The two uses, a speaker calling an audience to attention and a worshiper asking God to attend to a cry, are the same act of close listening pointed in different directions, which is why they belong to one word.