This short prophetic book dates from the early years of Josiah's reign over Judah (640-609 BC). Zedekiah was a descendant of Hezekiah, possibly the righteous king of that name (ruled 715-686). But this is not certain. His father was "Cushi" (black). This confronts us with a racial question right at the start. Could Zephaniah have been of Ethiopian origin, or mixed race?
The only way this could have worked is if Cushi's father, Gedaliah (the same name as the later governor of Judah), had married an African woman. In that case Cushi would have been half-Israelite and half-African, and his son, Zedekiah, a quarter African.
So the first verse presents us with two controversies for scholars, which is a very good batting average for a minor book: was Zephaniah a descendant of a king? and was he of (partially) African descent? In both cases, there is no conclusive textual evidence, only two possibilities. And neither one of these has any bearing on the content of the prophecies.
Zedekiah was a contemporary of Jeremiah and Nahum. With these prophets, we move into the latter half of the 7th century B.C. We should note that there is a long silence -- at least 40 years, perhaps closer to 60 -- between the previous generation of prophets and this group. No doubt this is due in part to the long reign (697-642) of Manasseh, perhaps Judah’s worst king. Isaiah and other prophets may have gone into hiding during his reign. Some may have been killed before their words could be written down.
"The name of Zephaniah, 'Yahweh has hidden,' may indicate that the prophet was born during the time of the atrocities perpetrated by Manasseh" (C. F. Pfeiffer, "Zephaniah," The New Bible Dictionary, 1358).
At this time in the Near East, after conquering Egypt and destroying Thebes, Assyria succumbed to civil war (652 BC) and went into decline. Arab tribes from the desert subdued Edom and essentially put an end to Moab (Albright, The Biblical Period from Abraham to Ezra, p. 79). The Babylonians achieved independence from Assyria in 626 and, with the Medes, destroyed Nineveh in 612. With the world powers distracted, good king Josiah made sweeping reforms, removing idols and high places, even in parts of Samaria (2 Kings 23:19). He may have remained a nominal vassal of Assyria, but in effect he was asserting Judah’s independence (Albright, p. 80).
Zephaniah came of age in a different world from that of the 8th-century prophets. He never knew the divided monarchy or a vital northern Israel rivaling the southern kingdom, nor could he remember Jerusalem besieged and desperate at the hands of the Assyrians. He lived in the last flowering of Judah's independence. Yet his message is surprisingly similar to that of his predecessors, sounding almost all of their themes.