“Spitting in your palm and shaking hands”

RORY: Plus Paris decided to let me split the debate time with her.
LORELAI: Wow! [pause] Wait, why am I wowing?
RORY: Because splitting debate time with Paris is like doing that whole “spitting in your palm and shaking hands” friendship oath thing.

Spitting in your palm and shaking hands is a common way to seal a deal between children (and certain adults), less dangerous than a blood oath, but still conveying a very serious bond.