You can think of a retainer as the one whose whole job is to keep something from leaving. Something wants to drift away — teeth that want to move back, a part that wants to slide out, a lawyer who might take another client, a room that could be rented to someone else — and the retainer is what holds it where it is. Ask what is being held, and you usually have the meaning.
Wiktionary records retainer as retain + -er — the -er that names the person or thing that does something. So the word is literally the one that retains, and every modern use is a different answer to the question of what is being retained.
來源字典把 retainer 拆成 retain（留住）加 -er（做這件事的人或東西），所以字面就是「會留住東西的那一個」。今天的每個意思，都只是對「留住什麼」給了不同的答案。
Wiktionary, English entry 'retainer' (packet source_ref kaikki:3f6f69a190036ae4:966000018:18594): 'From retain + -er.'
Three branches
把東西留在原位的物件
這一組最接近字面：retainer 是一個看得見、摸得到的東西，功能只有一個——讓旁邊那樣東西不要跑掉。
noun · B2
A small object made of plastic and wire that you wear inside your mouth, usually after braces come off, so that your teeth stay in the straight position they were moved into.
維持器
先付錢，把人或位子留住
被留住的東西變成抽象的了：一個人的時間、一個房間的使用權。留住的方法從夾住、扣住換成了付錢。
noun · C1
An amount of money that you pay a lawyer or another professional in advance, so that they go on working for you, or stay free to work for you when you need them.
預付聘金
被留在身邊的人
被留住的變成一個人本身，而且留的時間是一輩子；這一支是舊時代的用法，現代英文幾乎只在小說裡看到。
noun · C1
An old use: a servant, especially one who had worked for a rich or powerful family for many years and was counted as part of that household; also a follower who stayed at the side of an important person.
家僕；隨從