Is the period after the Bronze Age, when at the same time around the world, the great intellectual, philosophical, & religious systems that came to shape subsequent human society emerged—with the ancient Greek philosophers, Indian gurus (creators of of Hinduism & Buddhism), Persian Zoroastrianism, the Hebrew Prophets, the “Hundred Schools” (Confucianism & Daoism) of ancient China.

The phrase originated with the German philosopher Karl Jaspers, who noted that during this period there was a shift—away from more predominantly localized concerns and toward transcendence.

Transcendence means “to go beyond.” In the case of the Axial “revolution”, “going beyond” has several meanings:

• a shift to thinking about the cosmos and the way it works rather than taking for granted that it works
• the rise of second-order thinking about the ways that human beings operate, realising both that we are lying to ourselves and that we can improve ourselves. 

It's why the transcendent thinkers of the Axial Age: Buddha, Plato etc ... are still relevant today.

Second order thinkers ask themselves the question “And then what?” It is a form of meta-cognition that allows for investigation of our own thinking.

It became a thing during the Axial Revolution, when writing allowed us to store our thoughts, reflect on them and communicate with others across time and space.

As people started trading more and more during the ancient times, money became used. And coinage was a massive cognitive upgrade:

• Money popularises abstract thought. Accepting an abstract representation of value was a massive shift for the time.
• Money makes people think mathematically.