The works
Heron's surviving treatises are practical: the Pneumatica on devices worked by air, water and steam; the Automata on self-moving theatrical machinery; the Dioptra on a surveying instrument and its use; the Belopoeica on artillery construction; and the Metrica on measurement, which includes the formula for the area of a triangle from its three sides that still carries his name.
Together they are the fullest picture we have of Alexandrian applied mechanics, and they matter to this platform mainly for artillery and surveying, where they transmit the calibration rules that Hellenistic engineers actually used.
The aeolipile
The Pneumatica describes a sphere made to spin by steam escaping from bent nozzles. It is regularly presented as a steam engine that antiquity failed to exploit.
That framing is anachronistic. The device produces rotary motion with no mechanism for taking work off it, no boiler pressure worth the name, and no metallurgy behind it. It sits in a book of curiosities and temple effects alongside self-opening doors and singing birds, which is where it belongs. The interesting question is not why nobody built a locomotive but why a culture with this much mechanical skill directed it at wonder and theatre.
Dating
Heron's dates were long uncertain and are now generally fixed to the first century CE by his own reference to a lunar eclipse that can be identified astronomically. That is an unusually secure date for an ancient technical author.