院 pairs the wall radical 阝 with 完 (complete, also the sound): grounds completely enclosed by walls — a courtyard. Chinese architecture thought in courtyards, so institutions became 'courtyards' too.
院 is anywhere serious behind walls: 医院 (hospital), 电影院 (cinema — 'electric-shadow courtyard'), 学院 (college). The Beijing 四合院 — the four-sided courtyard house — is the architectural soul of the old city: life arranged around a private square of sky. Even the State Council is 国务院, the 'courtyard of national affairs'. In China, importance gets a courtyard.
Walls 阝 making a space complete 完 — a COURTYARD, an INSTITUTION.
电影院 'electric shadow courtyard' — even the cinema is architecturally a courtyard in Chinese.