'Ramadan Kareem' is a greeting used by Muslims during the holy month of Ramadan. The term 'Ramadan' refers to the ninth month of the Islamic calendar, a period of fasting, prayer, reflection, and community. 'Kareem' in Arabic means 'generous'.
Thus, 'Ramadan Kareem' is a way of wishing someone a 'Generous Ramadan', or interpreted as wishing someone bountiful blessings during Ramadan.