Yikes, watts and amp hours mixed!
So if you have an appliance that draws 1000watts, first, you have to know the voltage. Is it a 12v DC appliance or is it a 120 volt AC appliance? It matters. If its a 12v appliance, it will draw approximately 83 amps from the battery bank(which is a lot from almost any battery bank if it's for a sustained period of time) You can do the math, but a 1000amp hour battery bank could only sustain this kind of draw for about 6 hours before being depleted about 1/2 way which as has been mentioned is about as far as you should regularly discharge deep cycle batteries ( and less is always better for battery life)
If its a 120VAC appliance it will need to be connected to a device called an Inverter. An inverter is a device that converts DC voltage to AC. Inverters are at best about 90% efficient, so it would actually draw more and that would have to be factored in.
Also, as has been mentioned, batteries are normally rated at what is called a "20 hour rate" meaning if a given battery is a 200 amp hour battery, it is rated to be able to deliver its 200 amp hours over a period of 20 hours. That means 10 amps for 20 hours. If one draws power more quickly from the battery it should normally be expected to provide less than at the rated rate and this would be from a perfect, brand new battery. Each time a battery is cycled it permanently loses some of its capacity. Deep cycle batteries lose the least and the less the battery is drawn down before it is recharged reduces this as well. Battery manufacturers publish graphs that show their battery's performance at different discharge rates and different temps.
After all of this, you would want a way to recharge that bank within a reasonable period of time. Depending on the battery chemistry chosen, you would want at least a 100 amp battery charger for a 1000AH battery bank, but much bigger would be even better. As big as it sounds, even a 100 amp charger could take 8-9 hours to replace that 500AH of drawdown.
Ken