@SpehroPefhany is right about the LED. There is also another non-ideal component in the circuit: the battery. All real power sources will have an internal resistance that will limit how much power you can get out of them. You can model the battery as a an ideal voltage source in series with a resistor.
(The answer to the important question of when you get the most power out of a battery is: when the external resistance in the circuit is equal to the internal resistance. See Impedance Matching.)