It is a public db. There are nodes which relay candidate transactions and also special validator nodes which use an iterative process to come to a consensus on candidate transactions that will be included in the ledger. I believe the nodes hash the resulting set of candidate transactions and compare the hashes among themselves until there is a supermajority in agreement. There is no reward for running a node or a validator node.
So much for cryptos... a non-crypto is kicking our ass right now. Let's wait and see...