In short, the Persians created a monarchy. They had a king, who was simply called "the king" in the ancient world. The point was that he was "the king," that is "the great king." He was supposed to be a quasi-divine figure. From this perspective, we can say that the Persians created a sacred kingship.
The Persians were also very organized and structured. They created a system of local governmental officials, called satraps. These satraps ruled over a region called satrapies (there were twenty of them). What made their government even more successful was their custom of giving a lot of autonomy to the people they subdued.
As for communications, Cyrus (amazing as it sounds) created a courier, or mail system. Darius I continued this legacy and built a network that connected most of the empire. From Sardis (the Western-most city) to Susa (one of the capitols), there was a road of 1,600 miles. On this road the Persians also created places for lodging, supplies, and fresh horses. Communication was enhanced immensely.