What did the recurring statement, "there was no king in israel," really mean? use complete sentences.

Not only did the nation of Israel not yet have a king, but everyone lived as if they had no guidance or leadership.  If you read the next part of that sentence as recorded in the Book of Judges, you'll see the meaning:  "In those days there was no king in Israel; everyone did what was right in his own eyes" (Judges 21:25 New American Standard Version).

The days when God sent judges (leaders) to intervene in Israel's history were days when the people forgot the leadership of God and lived like they had no leadership.  They needed strong leaders from God (the judges) to guide them back to strength and to faithfulness.