The book takes place in Ancient Judah, during the span of Jeremiah's prophetic mission—from roughly 630 to 580 BCE. It's a time of immense suffering, warfare and destruction. The destruction of the northern kingdom of Israel had happened around 740 BCE, when the Israelites were conquered by the Assyrian Empire and the people sent off to live in Assyria. (These are the Ten Lost Tribes you've heard about.) The Judean kings of Jeremiah's time were probably intimately familiar with what had happened to the northern kingdom, since some of the people had fled south into Judah.
King Josiah, who ruled in the mid-seventh-century BCE, had tried to return the people to following God's laws. The High Priest Hilkiah, assumed to be the father of Jeremiah, had discovered a scroll of Jewish law during a renovation of the Temple in Jerusalem, which had fallen into disrepair and was being used to worship Baal. In the Temple. Are you kidding us? Anyway, Josiah recognized the scroll as the laws given to Moses at Mt. Sinai, possibly a copy of the Book of Deuteronomy. He outlawed idol worship, returned the Ark of the Covenant to the Temple in Jerusalem and threw out all traces of idol worship. He killed any pagan priests living in Judea along with their followers.
So far, so good. But later kings didn't enforce Josiah's reforms and the Judeans were soon back to their pagan, Baal-worshipping ways. And in 586 BCE the Babylonians invade, burning the Temple and Jerusalem to the ground and dragging most of the Judeans into exile. Jeremiah explains why all this is happening, lending a sense of order and justice to a time that likely seemed very chaotic.
Jeremiah sees the kings of Judah degenerate from the benevolent and just Josiah to incompetent and rather bad kings like Jehoiachin and Zedekiah. He continually tries to show them where they're going wrong, but no luck and no more second chances. The course of history is set. But his prophecies proved valuable for the people living in the aftermath of the exile and during the release from exile.
For a small geographic area, Judea was of great interest to the major powers that surrounded it. Because of its strategic location along the sea and trade routes, it was always at the center of conflict between the larger ancient kingdoms of Egypt, Assyria, and Babylon. But the Hebrews, who probably started to arrive around 1200 BCE, managed to stay there until the Babylonian exile.