If you Google the term or its cousin local church autonomy, you'll come up with results that are about half-and-half Baptist and Church of Christ in origin.
And while the links that I've pursued usually give at least some note to the idea of being under the Lordship of Christ, virtually all of them that I've seen define the terms exactly the way that any dictionary would: these terms mean that individual congregations govern themselves.
Yet the terms themselves do not appear in scripture.
They are not commanded. They are not exemplified. They cannot even be necessarily inferred. (Go ahead. Convince me.)
However, the terms "kingdom of God" (65 instances), "kingdom of heaven" (31 instances - all in Matthew!), and even "kingdom of Christ" (1 instance, Ephesians 5:5) are all over the New Testament.
Clearly, the history and prophecy of the Old Testament points to God establishing His kingdom in a powerfully redemptive way. He was to be Israel's king, but was rejected; nevertheless, He promised to establish an everlasting kingdom through men who were lineage markers in it for thousands of years.
He made good on the promise through His Son, Jesus, the Christ. The King.
How does that work with the governance of churches within His kingdom? We're a little fuzzy on that concept, aren't we?
I did a series of posts years ago touching lightly on what scripture says about living as a kingdom Christian:
Matthew | Mark | Luke | John | Acts | Ethic | King | Subjects
But what does it mean to be a kingdom church, governed by God and His Regent, Jesus Christ?
For to us a child is born, to us a son is given, and the government will be on his shoulders. And he will be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace. Of the increase of his government and peace there will be no end. He will reign on David's throne and over his kingdom, establishing and upholding it with justice and righteousness from that time on and forever. The zeal of the LORD Almighty will accomplish this. ~ Isaiah 9:6-7
Nothing in scripture gives me any indication that God expects His people as a nation nor as a church to fully govern themselves.
He gave instructions to Moses to have the people appoint judges (Deuteronomy 16:18), but He also gave Israel the Urim and Thummim so they could ask Him (Exodus 28:30).
He gave Israel the kingship they craved (1 Samuel 8:22) after having warning them about the way in which such a king should lead, many years before that (Deuteronomy 17:14-20) - and the future kings were to respect God's law; His instructions.
He gave the church of century one apostles and elders and evangelists and prophets to instruct Jesus' new followers after the ascension of their Example to the throne in heaven. They were to teach, instruct, and - among other things - resolve questions (Acts 15:2). But He also gave that church His own Holy Spirit, to guide them into all truth (John 16:13). In resolving the question of Gentile Christianity, the Holy Spirit was regarded as indispensible (Acts 15:28).
This is the same Holy Spirit about whom Jesus said we need to ask the Father in heaven in order to receive (Luke 11:13).
So when it comes down to the issue of church governance, there's a really important question that I fear is too often left unanswered, ignored, and sometimes even mocked in this century twenty-one:
Do the leaders - and members - of the church ask for Him?