What does Acts 14:16 mean?

Paul is trying to introduce the true God, the Creator of the universe, to a mob who insists on offering sacrifices to Barnabas as Zeus and Paul as Hermes (Acts 14:11–15). This short statement has a great deal of depth behind it.

From very early on, when the story of God's provision for Adam and Eve was only a few generations removed, the worship of God should have permeated the culture. Instead, people rejected God and embraced evil (Genesis 6:5). Even after God chose the Israelites to be His own people and His representatives on earth, mere decades after God rescued them from slavery in Egypt and miraculously provided for them, the Israelites followed in that evil tradition (Judges 2:11; 17:6).

The Israelites had no defense. God gave the Mosaic law to show them how to properly interact with Him. The Gentile nations had less information but also less obligation. God revealed Himself in nature such that Gentiles should have at least understood He existed (Romans 1:19–20) and pursued Him from that starting point. Beyond that, Gentile nations were only responsible for the information they had.

Nations related to the Israelites, such as those who descended from Lot and Esau, were expected to have a brother-like loyalty to Israel. Edom was the nation which came from Esau, the literal brother of the patriarch of Israel. They refused to let the fleeing Israelites pass through their territory on the way to the Promised Land. When Babylon attacked Jerusalem, Edomites handed their fleeing kinsmen to the Babylonian army (Obadiah 1:10–14). On other occasions, Edomites coordinated with Tyre to enslave the Jews (Amos 1:9–10). In return, God promised to destroy them (Ezekiel 35:7–9). Despite the Herods being from the line of the Edomites, they were destroyed the same time the Romans sacked Jerusalem in AD 70.

Nations that were not related to Israel but had long-standing relationships with them, like Egypt, Philistine, Tyre, and Sidon, were expected to respect Israel's God and therefore respect Israel. Even the Pharaoh Neco understood that the God of the Jews called him to fight the Babylonians but not Judah (2 Chronicles 35:20–21). God often used these nations to discipline Israel, but when they went beyond what God intended or disrespected what they knew of Israel's God, God punished them. When Pharaoh elevated himself above God, God promised to decimate Egypt (Ezekiel 29:3, 10). When Tyre assumed the deity of God (Ezekiel 28:2) and enslaved the Jews (Amos 1:9–10), God prophesied the city's destruction by Alexander the Great (Ezekiel 26:3–6).

All nations, whether those related to Israel, long-time competitors with Israel, or those with little to no interaction with Israel were bound by two expectations: they must treat their own people justly and they must not be cruel in war. God humiliated Nebuchadnezzar in part because he did not show mercy to the oppressed (Daniel 4:27). In Isaiah 14:5–6, God condemned leaders who ruled "the nations in anger with unrelenting persecution." In war, God judged Syria for "threshing" Gilead—possibly meaning ripping open pregnant women—and vowed to kill their royal family and exile their people (Amos 1:3–5).

With the spread of the gospel and the near-universal access to the Bible, nations are without excuse. God does not expect any nation to be a theocracy. He does expect rulers to be just in their governing and reasonable in war. Those who understand His expectations and respect Israel will be even more blessed (Genesis 12:3).