In English usage, a proper adjective is an adjective

Adjective

In grammar, an adjective is a 'describing' word; the main syntactic role of which is to qualify a noun or noun phrase, giving more information about the object signified....

 that takes an initial capital letter. A common adjective is an adjective that is not a proper adjective. The term is used informally only; it is not used by grammarians or linguists.
In general, an adjective is a proper adjective if its meaning is "pertaining to "x", where "X" is some specific person, place, language, or organized group.
Most proper adjectives are derived from proper nouns; for example the proper adjective Japanese is derived from the proper noun Japan.