One of the key things to keep in mind, when speaking about the accomplishments of the Han Dynasty, is that it did not emerge out of a vacuum. Quite on the contrary, it in fact built off of the earlier achievements of the Qin Dynasty, which carried out the unification...
One of the key things to keep in mind, when speaking about the accomplishments of the Han Dynasty, is that it did not emerge out of a vacuum. Quite on the contrary, it in fact built off of the earlier achievements of the Qin Dynasty, which carried out the unification of China under the first Emperor, Qin Shi Huang. Under the Zhou, China had disintegrated politically, entering into a period of endemic civil warfare. The Qin conquered their political rivals, and carried out a project of centralization and bureaucratization within China. This legacy would be continued under the Han, and proved critical to their lasting success.
However, the Qin were also notoriously brutal in their governing policies, exacting heavy taxes upon the peasants, and imposing a highly punitive legal and judicial system shaped on legalist principles. This brutality ultimately proved self destructive, however, as the dynasty would not long survive the death of its founder, quickly giving way to the Han.
Thus, when looking at the Han, you might get a sense that the Han maintained a lot of the bureaucratic and administrative reforms earlier set in place by the Qin, while curbing much of its brutality. Particularly notable in this, and deeply influential within the longer course of Chinese history, was the transition from a government based in the precepts of Legalism to one based on the precepts of Confucianism. It was the Han that established Confucianism as the political ideology of the Chinese State. I would suggest this innovation proved critical in ensuring the Dynasty's stability, particularly when compared against the Qin. Legalism, as a political philosophy, tends to be brutal, in the ways in which it views crime and punishment, and its advocacy of policies based largely in coercion. Confucianism, by contrast, places its focus on proper moral behavior, understood in terms of the duties and obligations which people owe each other. Such a radical transition in political philosophies (I suspect) would have likely played a role in the Han Dynasty's political success in ruling China for so many years.