Price elasticity of demand refers to the extent to which consumers will be sensitive to changes in price. If the price of a good or service increases and consumers buy much less of the product in response, the demand for the product is relatively elastic. If the price rises and consumers do not change their consumption patterns very much, the demand for the product is relatively inelastic.
There are a number of factors that help to determine how elastic the demand for a given product is. One of those is the amount of time at which we are looking. In general, the longer the time frame in question, the more elastic demand will be. If we look at the example in the question, we can see why this is so.
Let us say that the price of electricity goes up greatly. In the short run, there is not much you can do about it. You can turn off your lights more often or turn down the thermostat, but that is not likely to make a huge difference in how much electricity you use. But, in the long run, you can make a lot more changes. You can buy a new refrigerator that uses less power. You can put more insulation in your house. Because you have the longer time frame in which to do so, you can make more changes that will reduce your consumption of electricity.
This is why the demand for electricity in a year will be more elastic than that in a month.