This verse, "Grace to you and peace from God our Father and the Lord Jesus Christ," is a standard greeting used by the Apostle Paul (and others in the New Testament) in his letters. It's more than just a polite salutation; it's a powerful blessing and sets the tone for the rest of the letter. Let's break it down:

"Grace to you...": "Grace" in the New Testament, particularly in Paul's writings, refers to God's unmerited favor. It's a free gift of love, forgiveness, and acceptance that we haven't earned and don't deserve. It's the very foundation of our salvation. So, Paul is essentially praying that God's undeserved kindness and favor would be bestowed upon Philemon and his household.

"...and peace...": "Peace" (Greek: eirene, Hebrew: shalom) is more than just the absence of conflict. It signifies a state of wholeness, well-being, harmony, and reconciliation. It's a deep inner peace that comes from being reconciled to God through Jesus Christ. It also implies peaceful relationships with others and a sense of security and contentment in life.

"...from God our Father...": This highlights the source of both grace and peace. They are not human inventions or accomplishments; they originate from God the Father. This emphasizes God's paternal care and love for believers. He is the one who initiates and provides these blessings.

"...and the Lord Jesus Christ.": Jesus Christ is also mentioned as a source of grace and peace. This underscores His divinity and His crucial role in bringing these blessings to humanity. Jesus is the mediator between God and humanity, and it is through Him that we receive grace and peace. The title "Lord" acknowledges His authority and sovereignty.

In summary, the verse is a prayerful blessing that Paul bestows upon Philemon, wishing him God's undeserved favor and a deep sense of wholeness and harmony. It emphasizes that these blessings come from both God the Father and the Lord Jesus Christ, highlighting the central role of the Trinity in the Christian faith and the importance of the relationship to both Jesus and God.

Significance:

Sets the tone: Establishes the letter as one rooted in God's grace and peace.
Expresses Paul's care: Shows his genuine concern and affection for Philemon.
Reminds of God's provision: Grounds believers in the reality of God's unearned and transformative love.
Points to the Gospel: Serves as a concise summary of the Christian message of grace and reconciliation through Jesus Christ.

This greeting reminds readers of the fundamental truths of the Gospel and the source of all true blessing in their lives.