Proof of Stake protocols function by choosing transaction validators in a way that takes into account the size of their stake in a particular cryptocurrency.
Proof of Stake (PoS) is a fault-tolerant mechanism for achieving consensus. With this approach, block validators are selected based on how many coins they are staking. In this context, staking in means when validators commit funds to the system.
With Proof of Stake, validators need to lock their coins before they can take part in creating new blocks. At this point, these locked coins are used as collateral, so unscrupulous validators can't win. They end up getting barred from the network and also lose their stake. The network rewards honest validators when they forge new blocks and punishes those who try to cheat the system. This approach is great for generating trust with all concerned.
Many popular blockchains like bitcoin use the Proof of Work (PoW) approach, and Proof of Stake was designed to be a viable alternative to it. With Proof of Work, the validators must solve a complex mathematical algorithm to get their award, and doing so gains them permission to append the next group of transactions to the blockchain.
The downside of this approach is that to get into mining you need to buy and maintain a lot of very expensive and very specialized computers. Not to mention the fact that miners face massive competition. It's an extremely wasteful method that consumes a lot of resources.
In contrast, validating Proof of Stake blockchains just comes down to factors like the age and size of the coins being staked, and random selection process that ensures validators take it in turns to create new blocks.
Being able to validate transactions in a Proof of Stake blockchain with off-the-shelf computers is a huge advantage. Went just about any device will do it makes Proof of Stake systems more scalable, energy-efficient, secure, and decentralized.
Custom variations also exist, including Leased Proof of Stake (LPoS) and Delegated Proof of Stake (DPoS). Finally, there are hybrid consensus systems like Hybrid PoW/PoS, which blends features from both approaches to validation.