Servers running the XRP Ledger software keep a copy of the latest state: who holds what, which offers are open, which settings are on. You do not edit that copy by hand. You sign a transaction — a payment, a trust line, an offer — and a server shares it with the rest of the network.
Validators then run consensus. They propose sets of candidate transactions and listen to validators they have chosen to trust, a Unique Node List. When a supermajority of that list agrees on the same set, every server applies those transactions in the same order, under the same rules. The result is one new ledger version. If two payments try to spend the same funds, the rules keep one and reject the other. That is how the ledger stops a double spend without a single clerk in the middle.
A validated ledger is the one the network has agreed on. Until then, a payment can still fail. After that, it is final in seconds, not after a long mining race.
Real example: the ledger docs describe this loop — last validated ledger, agree on the next transactions, apply them, validate again. Sources: Consensus Protocol, Ledger Structure.