In this passage, the king of the South refers to Alexander's general Ptolemy and his descendants, who ruled Egypt. The king of the North refers to Alexander's general Seleucus and his descendants, who ruled Syria and Mesopotamia.
After Alexander's death, the kings of Egypt and Syria fought for control of Palestine, a strategically important land. The holy city and its people were caught between these two powers. These battles continued until their predetermined end (Daniel 11:27, 35, 40, 45; 12:1, 7).
Historical accounts of these events appear in 1, 2, and 3 Maccabees and in the works of Herodotus, Livy, Polybius, Porphyry, and Josephus.