A full node downloads the chain, verifies every signature and balance itself, and rejects anything invalid regardless of what miners or validators claim. It does not need permission and does not earn rewards.
Nodes are where the rules actually live. In a chain-split, the version of history that survives is whichever one the nodes people run choose to accept, which is why "run your own node" is more than a slogan.
Practically, most traders use a hosted node through their wallet or an API provider. That is fine for convenience, but it means you are trusting the provider's answer about your balance rather than checking it yourself.
Related: blockchain, consensus-mechanism, chain-split, block-explorer