A process to appoint the node which gets to create the next block. These nodes are called Validators in PoS based systems. Validators are chosen with regard to the amount of staked tokens attributed to them. These tokens (also referred to as "stake") are locked in the network and are comparable to a security deposit since they can be forfeited in the case of misbehavior by the validator. The amount of staked tokens determines the likelihood of the validator being chosen to create the next block. In order to not only favor the wealthiest ones, additional methods are also included in the selection process such as a pseudo-random lottery.
There are subforms of PoS, such as 'Delegated PoS (DPoS)', 'Liquid PoS (LPoS)', 'Bonded PoS (BPoS)', and 'Nominated PoS (NPoS)', in which token-holders can still participate in the security and maintenance of a blockchain without having to actively operate a node. They can simply transfer the validation-rights contained in each PoS token to another party. The two parties then share rewards and fees in a pro-rata fashion.
Blockchains are run and maintained by a decentralized, globally distributed network of nodes and not a central entity. Hence, a mechanism is needed that helps this network, often-times consisting of unknowing or untrusting parties, to establish security, validity, and guaranteeing availability. Currently, there are two main mechanisms, namely Proof-of-Work and Proof-of-Stake, that are used in blockchain networks to provide for security through economic incentives and cryptography. Furthermore, these mechanisms help to appoint the next node which gets to add a new block to the blockchain.