The Late Period includes the last native rulers of Ancient Egypt and (as with the Third Intermediate Period that it follows) it feels rather more arbitrarily grouped together as a “period” than earlier Kingdoms.
It begins in 664 BCE with the conquest of Egypt by the Assyrians. They install a puppet king, Psamtik I, who doesn’t remain a puppet for very long. He founded the 26th Dynasty, also known as the Saite Period after their capital in Sais. This lasts until 525 BCE when the Persians conquer Egypt for the first time under Cambyses II, who had himself crowned as Pharaoh inaugurating the 27th Dynasty. Another century or so passes before Darius II is overthrown and driven out of Egypt.
The last hurrah of Egyptian rulers of Ancient Egypt follows – three fairly short lived dynasties culminating in the rule of Nectanebo II the last king of the 30th Dynasty. There is then another brief period of Persian rule from 343 BCE to 332 BCE.
As you can see, it’s not a terribly coherent picture – a conquest here, a rebellion there, back again for more Persians and so on. But 332 BCE does mark a decisive change: Alexander the Great conquers Egypt as part of conquering the known world. There’s a brief hiatus here actually – before 332 BCE it is the Late Period, after Alexander’s death in 323 BCE we are in the Ptolemaic Period. In between it’s the Macedonian Period but as Alexander died young & without a clear heir it’s more of a pause for breath than a real period of history.