Someone cannot be there to handle their own business — a landowner is away, an abbey is not a person, an emperor cannot stand in every province. So a second person is handed the right to act in their name: to sign, to pay, to collect, to decide. Everything this word means comes out of that handover. The power sits with the person, but it was lent, and it can be taken back. That is why the same word can name a clerk who signs for a monastery and an official who can send someone to court.
From the word’s history
The supplied source traces procurator to Latin prōcūrātor, from prōcūrō, which is also the source of English procure; it is equivalent to procure plus -ator, and a doublet of proctor and procurer. So the word literally names the one who takes care of the business for someone.
資料裡說它來自拉丁文 prōcūrātor，源頭是 prōcūrō，也就是英文 procure 的來源；相當於 procure 加上 -ator，並且跟 proctor、procurer 是同源的變體。所以這個字字面上就是「替人把事情料理好的那個人」。
Wiktionary, "procurator"
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