Think of one small flat thing being pressed onto a bigger thing and made to stay: a label onto a box, a stamp onto an envelope, a seal onto a page. The Latin pieces inside the word say exactly that — ad- (to) plus figere (to fix), which you can still see as af- + fix. Two things follow from the picture. The piece being is minor on its own and only starts to matter once it is on something; and the joining is meant to last, not to be about and taken off again.
From the word’s history
Borrowed from Latin affixus, the past participle of affigere, which is ad- (to) plus figere (to fix). By surface analysis the English word is still af- + fix.
這個字借自拉丁文 affixus，是 affigere 的過去分詞，而 affigere 由 ad-（朝向）加 figere（固定）組成。從英文表面上看，它也還是 af- + fix，動作的畫面一直沒有走遠。
Wiktionary entries for affix (packet evidence): Borrowed from Latin affixus, perfect passive participle of affigere (from ad- + figere). By surface analysis, af- + fix.