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Physical = impact-based. Special = magic or energy-based. You can tell whether a move is physical or special based on whether a red "impact" icon or a gray eye icon is showed next to a move.
Attacks that can do damage are classified as "special" or "physical". So your pokemon's attack stat determines how strong its physical attacks are and it's special attack stat determins how strong its special attacks are. The same thing's with defence and special defence, it determins how well your pokemon can defend itself against physical attacks and special attacks, respectivly.