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1.
When you know someone well enough that you call them by their first name.
I had known Mrs. Jones so long I always called her Martha. We are on a first name basis.
by Jim The Clown Hater August 09, 2007
 
2.
When you no longer need to refer to someone by their last name. Usally used when 1. two enemies (particuarly Jocks) are trying to end a fight or if 2. an adult wants you to call them by their first name.
Draco Malfoy: Hey Harry
Harry Potter: What so now we're on first name basis?

you: You have a beutiful house Mrs. Smith
Mrs. Smith: Call me Wanda.
You: Oookay that's a little strange
by Beth Ryan August 07, 2007