Several parts combine into one character.

院 is a phono-semantic character: 阜 (阝, mound) for meaning and 完 (complete) for sound. Originally a large building or courtyard completely (完) enclosed by a wall (阝, a mound-like wall) — from which grew "a large building, an institution, a government office." The left 阝 means mound or wall.

Korean hanja-sound "won": 病院 (byeong-won, hospital), 學院 (hagwon, academy), 法院 (beobwon, court), 寺院 (sawon, temple), 大學院 (daehagwon, graduate school), 院長 (wonjang, director). Names of large institutions almost all end in ~院 (won).

Mandarin: yuàn, 4th tone. 医院 (yīyuàn, hospital), 学院 (xuéyuàn, college), 法院 (fǎyuàn, court), 电影院 (diànyǐngyuàn, cinema), 研究院 (yánjiūyuàn, research institute). 医院 (yīyuàn, hospital) is a daily Mandarin essential.

Japanese: on-reading イン (in) — no kun-reading (on-only). 病院 (byōin, hospital), 入院 (nyūin, hospitalization), 大学院 (daigakuin, graduate school), 美容院 (biyōin, beauty salon), 寺院 (jiin, temple). Note that Japanese 病院 (byōin) and 美容院 (biyōin) sound similar.

Memory aid: a large building completely (完) enclosed by a wall (阝) — an institution like a hospital or academy.