Camp derives from the French slang term se camper, meaning “to pose in an exaggerated fashion”.
The OED gives 1909 as the first print citation of camp as "ostentatious, exaggerated, affected, theatrical; effeminate or homosexual; pertaining to, characteristic of, homosexuals.
So as a noun, ‘camp’ behaviour, mannerisms, et cetera. (cf. quot. 1909); a man exhibiting such behaviour". Per the Oxford English Dictionary, this sense is "etymologically obscure".