Curse of the Walking Pox is a specific Aura card (a Curse enchantment), not a keyword ability—so it behaves like any Aura you attach to a player. When it enters, you choose an opponent to enchant. At the beginning of that player's upkeep, they lose 1 life, then create that many 1/1 black Zombie tokens (so they get one Zombie). It also has a sacrifice ability: sacrifice five other Curses to destroy all non-Zombie creatures.
The common misunderstanding is thinking it harms the controller or hits everyone—it only triggers on the enchanted player's upkeep, and only they make Zombies. Note "they lose 1 life, then create that many" tokens, so the count scales with the life lost, not a flat one.
In Commander, it's a slow, multiplayer-friendly Curse that pressures a single foe while building a Zombie army for a board wipe payoff if you go heavy on Curses.