Judges 3:14, "The children of Israel served Eglon the king of Moab eighteen years," means that for a period of eighteen years, the Israelites were under the political domination and oppression of Eglon, the king of Moab. It was a time of servitude and subjugation where they likely had to pay tribute, obey Moabite laws, and were subject to Moabite rule.

Here's a breakdown:

"The children of Israel": This refers to the Israelites, the descendants of Jacob/Israel, who had settled in the land of Canaan.

"Served Eglon the king of Moab": This signifies political subjugation and servitude. It implies the Israelites were forced to be subservient to Eglon and his kingdom. This likely included:
Paying tribute/taxes: They would have had to give a portion of their agricultural produce, livestock, or other goods to the Moabites.
Military service: They might have been forced to fight alongside the Moabites in their wars.
Obeying Moabite laws: They would have been subject to the legal system and dictates of Eglon's rule.
Loss of autonomy: They would have lost their independence and self-governance.

"Eighteen years": This specifies the duration of this period of oppression and subjugation. It was a significant amount of time, indicating a sustained period of hardship for the Israelites.

Context within the Book of Judges: The book of Judges is a cyclical narrative. The pattern is:

1. The Israelites turn away from God and worship other gods.
2. God allows them to be conquered and oppressed by their enemies.
3. The Israelites cry out to God for deliverance.
4. God raises up a judge (a leader and deliverer) to defeat the enemy and deliver Israel.
5. The land experiences a period of peace until the cycle repeats.

Judges 3:14 is part of this cycle. The Israelites had turned away from God, and God allowed Eglon, king of Moab, to conquer and oppress them as a consequence. This verse sets the stage for the story of Ehud, the judge who will eventually deliver Israel from Moabite oppression.