An analogy to motion: joules are distance, watts are speed, and watt-hours are like light-years.
The amount of energy consumed, if you have one watt of power for a certain amount of time, is the confusingly-named Watt-hour, or Watt-year, etc. 1 Watt-second is 1 Joule. 1 Watt-minute is 60 J. 1 Watt-hour is 3600 J.
I'm not really sure why the Wh exists, other than to let you easily estimate how much it costs to run an appliance for once hour. It tends to confuse.