adjective
[more ~; most ~]
correct according to social or moral rules
behaving in a way that is correct according to social or moral rules
always used before a noun :exactly correct
proper punctuation
always used before a noun :right or suitable for some purpose or situation
always used after a noun - used to emphasize that you are referring to the specific thing that is being named
Her family lived outside the city proper. [=lived in an area that was close to the city but was not actually in the city]
always used before a noun chiefly Brit :complete or absolute
proper to
formal :belonging to or suited to (something)
adverb
chiefly Brit informal :in a complete way