Proof Of Stake is another consensus mechanism that cryptocurrencies can rely on. The system is based on voting, and requires ownership of the related coins.
To put it in a simple way ... stackers (coin owners) get to create blocks and store transactions in them, in exchange for more coins. The bigger stack you own, the higher chance that you will be chosen to create the new block.
Strackers would operate so called Nodes or Master Nodes, so computers handling the actual transactions and storing full copies or parts of the blockchains. In order to be "allowed" to run a node, you need to deposit certain amount of said coin ... or in other words, stack it.