Cardano keeps balances as unspent transaction outputs (UTxOs), like individual banknotes. A transaction spends (consumes) some UTxOs as inputs and creates new UTxOs as outputs. The total of inputs must cover outputs plus the fee.
'Extended' means outputs can carry a datum (data attached to the output) and be locked by a script. To spend a script-locked output, the transaction supplies a redeemer, and the script checks the whole transaction context.
Because a transaction states exactly which outputs it consumes, its result can be checked before submission: it either applies as built or is rejected, and fees are predictable.
Try the interactive eUTxO simulation.