The arm — the part of the body from the shoulder to the wrist.
彼は腕に大きなタトゥーがある。
He has a large tattoo on his arm.
荷物が重くて腕がだるい。
The luggage is heavy and my arms feel tired.
赤ちゃんは母親の腕の中で眠った。
The baby slept in the mother's arms.
Skill, ability, or talent — used to refer to someone's competence (e.g., 'good at', 'improve one's skill').
彼は料理の腕がいいのでレストランで働いている。
He's skilled at cooking, so he works at a restaurant.
毎日練習してピアノの腕を上げた。
He improved his piano skills by practicing every day.
新しい仕事で腕を試してみたい。
I want to try my skills at a new job.
Physical strength — sometimes used to mean arm strength or physical power.
彼は腕の力だけで箱を持ち上げた。
He lifted the box using only the strength of his arms.
力自慢の彼は腕相撲が得意だ。
Boasting of his strength, he is good at arm wrestling.