Proof-of-Stake (PoS) is a type of algorithm that determines distributed consensus in a cryptocurrency blockchain. In a PoS algorithm, users with the greatest stake in the system (accumulated age or amount of wealth) are preferred for creation of the next block in the chain. PoS is an alternative to Proof-of-Work algorithms, in which users perform computational tasks to earn the right to create the next block.
PoS algorithms use randomization to create fairness in the block selection process. Without randomness, the system would not be decentralized at all, because the largest stakeholders would act like a centralized bank.
Each PoS algorithm may use its own combination of pseudo-randomness and stake to select which account will forge the next block. For example, the Nxt cryptocurrency considers each token held in an account to be a unit of chance that the account will be selected. So, an account with two tokens will be twice as likely to be selected as an account with one token. To prevent fraud, the tokens must be held in the account for a minimum amount of time before they can contribute to the selection chance.
By contrast, the Peercoin cryptocurrency uses a concept of "coin age," in which stake is affected by the amount of time a coin is held in the account. When the account is selected for block creation, that coin age is expended, and the account must begin accruing coin age again from that point in time.