“A.F.A.M.” most commonly stands for:

• Ancient Free and Accepted Masons — a Masonic designation used by some branches of Freemasonry.

It refers to a form of Freemasonry organization that follows traditional rituals and structure. The letters indicate:

• Ancient
• Free
• Accepted
• Masons

In short, A.F.A.M. is a Masonic abbreviation for a branch of Freemasonry organizations.