入籍 (nyūseki) means “marriage registration”

More examples

結婚式の前に入籍する人もいます。kek kon shiki no mae ni nyū seki su ru hito mo i ma su

Some people register their marriage before the wedding.

Refers to making a marital relationship part of the official family-register record rather than simply celebrating a wedding.

入籍届を出すnyū seki todoke o da su
submit a marriage registration form
入籍の手続きをするnyū seki no te tsuzu ki o su ru
complete the marriage registration process

結婚に伴い、夫婦の身分関係を戸籍に記載すること。kek kon ni tomona i fū fu no mi bun kan kei o ko seki ni ki sai su ru ko to

入籍 (nyūseki) is formed from 入 (nyū, "enter") and 籍 (seki, "register"), expressing the idea of entering an official register.

In official contexts, 婚姻届 (kon'in todoke) is the form used to report a marriage, while 入籍 (nyūseki) describes the resulting family-register entry.