My appliance is 1000w, why does it need a generator which has 1600w？ 

Some appliances have identified their watt level. For example, hairdryer is identified as 1000w. This means the hairdryer itself will produce some heat energy of 1000w. But the electric energy hairdryer used is much more than the heat energy it can produce. The heat efficiency is not 100%. There are so many additional losses.
Another example, a watt level is 1100w’s microwave oven could produce 1100w’s energy while cooking. But it needs more power from the generator.