The foundation of derivatives pricing: if a portfolio pays exactly what the derivative pays in every future state, the two must cost the same, or there is an arbitrage.
Why this is the deepest idea in the subject. It removes probability from pricing entirely. You do not need to know how likely anything is; you need to know you can build it.
Where it breaks. Replication requires continuous trading with no costs and no gaps. Real markets have jumps, transaction costs and limits on shorting - which is why hedging is imperfect and why market makers charge for it.