What is the difference between energy and power?

Power (KW) is the instantaneous usage and Energy (kWh) is power that is used over time.  Toasters and things are rated in watts which is the power that they draws at any given moment.  A customers power consumption can change quickly as loads are turned on and off but energy accumulates gradually.  We bill customers based on the energy they use over time in these energy buckets called kilowatt hours (kWh). 
 
Power = Watts
Energy = Kilowatt hours (kWh)
* For you Americans remember that K = 1000 so 1 KW = 1000 W
 
Water Analogy
Power = Gallons per minute, flow rate.
Energy = Total gallons consumed.
If you stop using water the flow rate (power) goes to zero but your total energy stays the same, it just doesn’t get any higher.  The total gallons consumed (energy) is what we bill for.
 
Speedometer Odometer Analogy
Power = Speedometer (current speed)
Energy = Odometer (how far you’ve gone)
The speedometer (power) can quickly go from zero to sixty and back to zero, but your odometer (energy) will only slowly count up.  The odometer counts faster as your speed is faster over time.  The speedometer tells you how fast you are going right now (how much power you are using right now), while the odometer tells you how far you’ve gone (how much energy you’ve used in total).   So speed is to power (kw) as distance is to energy (kWh).
 
Graph Example
The Blue line is power (speedometer) and the Red line is energy (odometer).  Notice as the power (blue) increases the energy (red) line goes steeper.  If the power (blue) was zero the energy (red) line would be flat (no increase).
 
Grid Scale Battery Example

1. How much total energy can the system store? (Think watt-hours)  1250 kWh  / 1,250,000 Watt Hours

How much power can it deliver at any moment? (Think watts)  5 MW / 5,000,000 Watts