Planar cards are used when playing Planechase, a modifier that can be used for any match of any format.
When playing planechase, there's typically a single planar deck shared by all players. At the beginning of the game, the top card of the planar deck is revealed until a plane is revealed (there are also cards that go in the planar deck which are not planes). The static ability of that plane is now active.
At any time a player could cast a sorcery on their turn, they may pay any necessary costs and roll the planar die. The first time a player rolls the planar die in a turn, it's free. After that, the cost increases by {1} each roll. If the player gets the planeswalk symbol, the next card in the planar deck is revealed, and all players "planeswalk" to that region of that plane. If the player rolls chaos, then that player does the chaos effect on the plane.
Planeswalking to another plane does not use the stack, and cannot be responded to. By the time the new plane is revealed, players cannot respond to the plane changing.
In contrast, rolling chaos puts the ability on the stack so it may be responded to.