Proper means right and suitable for the situation — the accepted way. The proper procedure, proper shoes, do it properly.
In British informal English it is also an intensifier meaning real or thorough: a proper meal, a proper mess, a proper job. That use is very common in speech and does not travel to American English. Note proper noun, which is the grammatical term for a name and takes a capital letter, and the phrase the town proper, meaning the town itself as against its outskirts. And propriety, the noun, means correct behaviour.
1adjectiveproperRight and suitable for the situation.
“There is a proper way to do it and nobody follows it.”
2adjectiverealReal or thorough, in British informal use.
“Sit down and have a proper meal.”
3adjectiveitselfItself, as against the surrounding area.
“The city proper has about half a million people.”
Too few real examples of this word to estimate which sense is commonest.
proper is a quality of correctness.
Latin proprius meant one's own — the same root as property, appropriate and proprietor. Something proper was originally something belonging to you, and the sense of correctness came from the idea of what properly belongs to an occasion.
Proto-Indo-European
*preyH-
Anglo-Norman
propre
Middle English
propre
English, today
proper
From Middle English propre, from Anglo-Norman propre. From Middle English propre, from Anglo-Norman proper, propre, Old French propre (French: propre), from Latin proprius.
Etymology from Wiktionary, CC BY-SA