申 shēn to state

to report; to declare; to extend

How it came to be

象形 · Pictogram

A drawing of the thing it means.

Originally: lightning

The oldest form shows a bolt of lightning; the sign first wrote the words for lightning and for a god.

Bound; to state/declare formally. Star word 申请 (shēnqǐng), apply for: 申请签证 (shēnqǐng qiānzhèng) apply for a visa.
申报 (shēnbào) = declare officially (customs, taxes); 重申 (chóngshēn) reaffirm/restate.
All carry an official, procedural tone. You 申请 to an institution, not a friend.