Fire signals (here and here) were the fastest means of communications, but of course needed prearrangements (setting up the stations, fixing the code, etc.). They were mostly used in a military setting and certainly didn't have an application in the routine administration of ancient empires. Routine communications were conducted by ship and horseback. Slow and sometimes unreliable communication was counteracted in ancient empires by the delegation of authority. Thus the Achaemenid (Persian) Empire had semi-autonomous satraps and client kings, while the Roman Empire had far less-autonomous provincial governors.

Semaphore Towers were used just prior to telegraph lines. Its like flag signals taught to sailors today where certain positions would mean certain things (most commonly letters). It was developed as an attempt at communicating rapidly over great distances without using a horse rider or something that could be intercepted by brigands or highwaymen.

It was famously used when Napoleon after capturing Paris in the revolution used the towers to send a message "Paris is quiet and her citizens are at peace" (or something like that, i cant find the exact quote).