Babylonian society, culture and history are best reflected in the Enuma Elish. Numerous theories surround the creation and origin of this literary text, wherein it is theorized that the Enuma Elish was actually created during the reign of the Akkadians, prior to the rise of the Neo-Babylonian Empire. More than a creation story for the Babylonians, the Enuma Elish

… reflects an era when the city of Babylon had risen politically…as the traditional locus of divine power in the world and a new sense of nationalism had emerged with Babylon at the center of a world empire (Arnold, 2004:83).

Thus, the importance of Enuma Elish as a literary text that surfaced during Nebuchadnezzar's reign signifies only the richness of Babylonian culture, but also the emergence of a strong Babylon nation, strengthened and...

Nebuchadnezzar's reign was the peak of Babylonian glory, when Babylonians felt nationalism and prosperity -- culturally, politically, and economically.
In summary, the question, 'what is the Neo-Babylonian period' is best answered by its three more famous kings, Nebuchadnezzar's reign, and the Enuma Elish. The Neo-Babylonian period gave birth to the Neo-Babylonian Empire, dominating societies and kingdoms in the Middle Eastern region, and became a 'superpower' among allies and foes during the 626 BC- 539 BC).

References

Arnold, B. (2004). Who were the Babylonians? Brill Academic Publishers.

"Neo-Babylonian Empire." (2005). World Timelines web site. Available at: http://www.worldtimelines.org.uk/world/asia/western/1000-550 BC/NeoBabylonian.