In terms of historical fact, I think one can only answer this by saying, "they subjugated more territory". To move into the realm of informed speculation, we would do well to consider the realms that preceded it.

By far the most important, and one we know that at least Cyrus compared his realms to, was the Neo-Assyrian Empire (map), sometimes regarded as the first "true" territorial empire with an effective bureaucracy. Unfortunately I am not as well-versed in the details of it as I would like to be (for no better reason than the best books being really expensive...)

The Assyrian Empire at its height proved able to project force from Mesopotamia into both Anatolia and Egypt, so clearly, there was nothing unprecedented about that in principle. What lay to the east and Northeast of it, then? Well, the Iranian and Elamite city-states/tribal federations/whatever, and the "pre-Armenian" Urartu to the North.

Cyrus, as you'll recall, was the king of Anshan. If you look at various maps, you're very likely to come across a ridiculously bloated "Median Empire", encompassing all of Iran, Caucasia and Central Asia. In reality, the Medes, who may not have been a single political entity, probably did not rule more than Kurdistan and Armenia. It's probably easiest to look at a map of modern Iran: Link Cyrus' domain would probably have encompassed something like Khuzestan, Fars, Ilam and Luristan (and likely not as a single entity but through a complex web of diplomatic and familial relations with local nobility, etc.), and the Median domains encompassing something like Kermanshah, Qazvin, Kurdistan, Azerbaijan and whatever to the west-northwest of that.

Subjugating the Medes and invading Anatolia, subjugating Lydia, he then seems to have done what no Assyrian ruler could have done - expand to the east, into Central Asia, presumably via Tabarestan. The exact timeline is hard to reconstruct, unfortunately, but there is no doubt that Cyrus was in a unique position to project power in ways that no previous polity had really been able to.; the Assyrians had never subjugated anything east of the Zagros. And the rest is history.

But we would be amiss if I did not address what I always do - in an administrative sense, it may perhaps be said that Darius, not Cyrus, was the true founder of the Achaemenid Empire, though we cannot know for sure as we don't know how radical Darius' revenue-raising reforms were. I don't think it was as simple as effective taxation though, either - we cannot discount ideology and propaganda. Darius, like Cyrus, seems to have drawn on the Assyrian rulers, but his inscriptions also have a distinct rhetoric to them. His very name, Daraya-Wahush, or "One Who Does Good", underlines the moralist and theocratic nature of Persian propaganda and of their understanding of asserting Khshaca, the power of rulership.

If I knew Assyrian inscriptions better, I would be able to go further down this road, but unfortunately, it's a bit outside my comfort zone.

Still, I hope this at least gives you an idea of the circumstances that allowed the Achaemenid Empire to grow so powerful, and in what ways it was precedented, and not.