The Proof of Stake algorithm is a generalization of the Proof of Work algorithm. In PoS, the nodes are known as the ‘validators’ and, rather than mining the blockchain as in PoW algorithm, they validate the transactions to earn a transaction fee.
There is no mining to be done, as all coins exist from day one. Simply put, nodes are randomly selected to validate blocks, and the probability of this random selection depends on the amount of stake held. So, if node X owns 2 coins and node Y owns 1 coin, node X is twice as likely to be called upon to validate a block of transactions. The specific implementation of PoS can vary, depending on the use case, or as a matter of software design. Instances include Proof of Deposit and Proof of Burn. The PoS algorithm saves expensive computational resources that are spent in mining under a PoW consensus regime.