The Qin and Han were early dynasties of a unified China. The Qin dynasty ruled briefly, from just 221-206 BCE, but was important because it was the dynasty that first unified China. It had a rather authoritarian rule, and its harshness was part of the reason for its downfall and replacement with the Han dynasty. Among its other achievements, the Qin dynasty standardized measurements and invented the crossbow. But I think the answer you’re looking for is that the Qin dynasty’s signature accomplishment was the completion of the Great Wall to fortify, secure, and define its borders. It’s an accomplishment we still associate with China today.
The Han dynasty (206 BCE-220 CE) was a period of advancement in thought and culture in ancient China. Developments were made in iron-working and in methods of agriculture and engineering. But the most significant advance was the invention of paper for writing by Cai Lun in about 105 CE, although there is some evidence that paper was used earlier than that. Early paper was made from plant fibers and old rags. It was used for wrapping things as much as anything. But of course, given the importance of writing and the importance ancient China placed on preserving its history and other texts, the adoption of paper for writing is the most important achievement of this early period.
Note that China has a long history as a continuous civilization and a number of other key advances were made here. Gunpowder especially came from China (although much later than the Han or Qin) and has influenced the history of the world, perhaps more than any other invention.