Proof of Stake (POS) is fundamentally different from Proof of Work (POW) and relies on the core idea of selecting the next block producer (transaction validator) based on the amount that a given Pool has Staked. The idea being that, to produce a block, you need to hold a lot of ADA and thus have a big 'Stake' in Cardano, meaning you would need to control 51% of all ADA to commit a fraudulent transaction. This is mathematically proven to be secure assuming rational actors (to attack, you need to hold 51% and as soon as an attack is found, the value of the coin would plummet - thus an attacker would always lose money).