The way that you hold your hand while playing, and direction that you sling your beads is considered the "plane" that you are in. There are 3 primary planes. Other planes exist, but they are not named and usually only used for trick transitions.
Bike Plane[]
This is the most popular plane. You palm is facing your body. The beads are swinging in an up-and-down motion.
Wall Plane[]
The palm is facing "the wall" (to the left or right, depending on which hand). The beads are swinging in a side-to-side motion.
Floor Plane (0g)[]
The palm is facing the floor or ceiling. Commonly called 0g in balisong and other skill toys, slinging in floor plane is a fight against gravity.