Official term for a local immigration bureau or office handling entry/exit procedures, visa applications, and residence matters.
I went to the immigration office to pick up my new residence card.
出入国管理事務所 is a local office, while 入国管理局 is the Immigration Bureau (a higher-level organization).
Compound of 出入国 (entry and exit from a country), 管理 (management), and 事務所 (office).