Proof of Work and Proof of Stake are the two main ways a blockchain gets its network of computers to agree on what's true, without a central authority. PoW rewards computational effort; PoS rewards a financial stake. Both solve the same problem covered in \[pillar hyperlink: What Is Blockchain\], but they get there very differently.
PoW basics
In Proof of Work, miners compete to solve a difficult math puzzle. The first to solve it gets to add the next block and earns a reward, plus transaction fees. Solving the puzzle costs real electricity and hardware, which is exactly what makes cheating expensive. See Bitcoin Mining for how this plays out in practice.
PoS basics
In Proof of Stake, validators lock up ("stake") the network's own coin as collateral instead of burning electricity. The protocol selects a validator to propose the next block, weighted by stake size, and slashes anyone caught cheating. Users can also earn rewards by staking directly; see What Is Staking.
Energy and security
PoW's security comes from the sheer cost of hardware and electricity required to attack the network, but that cost means high energy use. PoS reaches similar security with a fraction of the energy, since the "cost" is capital at risk rather than power consumption. The trade-off is that wealth, not hardware, determines influence.
Which coins use each
Bitcoin is the largest and best-known Proof of Work network. Ethereum ran on PoW for years before switching to Proof of Stake in 2022\. Most newer major chains, including Solana, launched with PoS or a variant of it from the start.