In a Proof of Stake blockchain network nodes are run by users who are deliberately distributed across computers across the world. There is no central authority as the network aims to achieve full decentralisation. Running a node means running the protocol on a local or remote machine and conforming to the rules of the protocol.
Nodes compete with each other to complete blocks of verified transactions for the network. In return, they receive a block reward of newly minted coins. For instance, if you’re running an Ethereum node, you earn ETH. On Harmony you earn ONE But in order for participants to help the network and earn, they must ‘stake’ coins. This means holding them in a special wallet and keeping them there as long as they are running a node. This incentivises participants to act in the best interests of the network.
By having these nodes set up in a decentralized manner as described above, and by providing incentivization to keep the network operating smoothly and safely, PoS systems take the best of game theory and automation and combine them with a digital currency that can also be saved, spent or traded.
If you wish to learn more about nodes in general nodes.com is an excellent resource.