Answer:
Some have connections to their meaning, but most are phonetic.
中 CHUU, naka - middle, medium - China (中国)
韓 KAN - Korea (韓国/朝鮮)
亜 A - rank, next, come after, Asia - Asia (亜細亜)
阿 A, kuma, omoneru - mountain ridge, to flatter - Africa (阿弗利加)
欧 OU - Europe (欧州)