http://cleantechnica.com/2015/02/02/power-vs-energy-explanation/Watts is a unit of power, not a unit of energy.
Your question: "does that mean that the rig uses 850 watts of electricity per second? per hour? per 24 hour period?"
Is a bit like asking about your 285 peak horsepower vehicle, "does that mean that if I run the vehicle continuously at peak horsepower it uses 285 horsepower per second? per hour? per 24 hour period?"
For some reason the "horsepower" statement clearly sounds wrong, but people always seem to get confused about the power when the "watt" unit is used.
Now, when power is supplied for a period of time, you use up energy. Therefore an 850 watt unit that runs for 1 hour will use up 850 watt hours of energy (or 0.85 kilowatt hours). Your electric bill is almost certainly using the kilowatt hour unit of measurement.
Just like vehicle will use up a certain amount of fuel when you operate it at a particular horsepower for a specified unit of time (volume of fuel containing a certain amount of available energy). So if you run your 285 peak horsepower vehicle at peak horsepower continuously for an hour you will use up some number of gallons of fuel.
Run the vehicle for 10 hours, and you'll use up 10 times as much fuel.
Run the electric equipment for 10 hours, and you'll use up 10 times as much electricity (8.5 kilowatt hours).