A fully validating node downloads blocks, verifies proof of work and every relevant consensus rule, and maintains its own view of the spendable-output set. It does not need to trust a block explorer, miner or wallet server.
A node answers a narrow but powerful question: according to the rules its operator chose, which chain and payments are valid? Running one prevents third parties from silently substituting different rules or account information.
A pruned node still validates the chain from genesis but discards older block files after validation. It retains the current UTXO set and chain state, reducing storage at the cost of serving less historical data to peers.
For the clearest picture, read this entry together with Bitcoin, Timechain, Transaction, UTXO, Proof of Work. The reverse links also lead from Bitcoin, Timechain, Proof of Work, UTXO.