Proof of work (PoW), used by Bitcoin, secures the network through computational competition: miners race to solve a cryptographic puzzle, and the winner proposes the next block. Security comes from the cost of the hardware and electricity required to attack the network.
Proof of stake (PoS) replaces that computational race with an economic one. Validators are selected to propose blocks based on how much cryptocurrency they have staked, and security comes from the fact that misbehaving validators lose (part of) their stake. This is what makes 'staking' as an income-generating activity possible in the first place — PoW mining has no equivalent delegation mechanism for passive token holders.
PoS networks are generally far more energy-efficient than PoW networks, since there's no computational race to win — this was a major motivation behind Ethereum's 2022 transition from PoW to PoS (`The Merge`). The trade-offs are different too: PoS security depends on the value and distribution of the staked token itself, and introduces new design questions around slashing, validator selection, and stake concentration that PoW networks don't face in the same form.