Both (العربي) and (العربية) are adjectives meaning "related to Arabic or Arabic speaking countries". (ة) is usually added to the masculine form of the adjective to get the feminine form. Furthermore, feminine nouns usually end with (ة).
For example, you can say: ( الثـقافــة العـربيـة = َArab culture, الـطـبـخ الـعــربـي = Arab cuisine). As you can notice, (الثقـافة) is a feminine noun (because it ends with a 'ة') that's why we use the feminine form of the adjective (=الـعـربيـة). The same reasoning applies to the 2nd example ("الـطـبخ" being a masculine noun).