The head of gold is easy to understand - the Bible narrative itself clearly states that it represents King Nebuchadnezzar's own Babylonian kingdom (see Ancient Empires - Babylon) that conquered Jerusalem, destroyed the original Temple (see Temples) and carried the Jews, including the prophet Daniel, off into captivity about 586 B.C.
What about the rest of it? This is not difficult, secular history does a very good job of laying it out before us.
After the Babylonian "head of gold" came the Persian empire (see Ancient Empires - Persia). The Persians under their various kings, including Cyrus who allowed the Jews to return to Jerusalem, swept away the Babylonian empire. They are the "chest and arms of silver."
After about 2 centuries of dominance, the Persian empire was swallowed up by the Greeks under Alexander the Great (see Ancient Empires - Greece). Many consider Alexander to be the greatest military commander of all time, taking vast areas from southern Europe, across the Middle East and deep into southern Asia, all while a relatively young man. He reportedly died in his early thirties from an unknown illness. The Greeks became the "belly and thighs of bronze."
After the Greeks came the Romans, the "legs of iron" (see Ancient Empires - Rome). The Romans took the areas that the Greeks had, plus nearly all of the rest of Europe, including Britain. The Roman empire was of course dominant during the time of Jesus Christ.
History records that the Roman empire "fell" in the fifth century after Christ (over the last 15 centuries both the Roman empire, and the Roman church, suffered "mortal wounds" - from which they both recovered), but it actually came back alive as the so-called "Holy Roman Empire." It called itself "Roman" because it claimed succession to the ancient Roman empire, and "holy" because it held control over mainstream European Christianity. It was as much political as it was religious - the church was the state (which matches exactly what is coming in Revelation 13), often involving a see-saw power struggle between popes and emperors:
On February 2, 962, Pope John XII crowned Otto I as the Holy Roman Emperor. When Otto succeeded his father Heinrich (Henry) as German king in 936, the people raised their right hand to show approval and shouted "Sieg und heil" ("victory and salvation"). Most historians view 962 as the beginning of what would later officially be known as the Sacrum Romanum Imperium Nationis Germanica ("the Holy Roman Empire of the German Nation") - the First Reich. Other Reichs followed right up into the twentieth century.
The octagonal imperial crown of the Holy Roman Empire, made especially for the coronation of Otto, became the very symbol of European unity for centuries to come. In recent years, Otto von Habsburg (whose ancestors were some of the Holy Roman emperors, and whose oldest son, Karl, is the now the potential heir to that heritage) called attention to the possible role of that crown of the Holy Roman Empire in the new European Union (although Britain is today a member of the EU, it will almost certainly withdraw later in favor of an alliance with the United States and Canada) - which will actually be an extremely powerful reawakening of the old Europe. The last revival before The Return Of Jesus Christ.
Fact Finder: Who will be the great end-time antichrist?
See The Antichrist