A validator is a receiver of blocks from the Ethereum network and then does the transactions re-executions to make sure that the block is valid. The mechanism is called proof-of-state (POS). The validators have exclusively allocated funds in the network in ETH form and replaces the miners work done in the proof-of-work. In securing the network, users must buy and hold cryptocurrency in order to be selected to validate blocks and receive gas fees.
Your transactions will only be processed once the payment was guaranteed by paying a gas but it does not guarantee the success of the transaction.
The following is an example scenario of an unsuccessful transaction even if you have already paid the gas fees: If there is high activity on Ethereum, gas prices fluctuate when a popular NFT is released, due to congestion in the network the gas prices rise and the amount of gas fee that you paid may no longer be enough for the validators to process and approve the transaction.