First, please note that economists do not recognize the idea of "price gouging." Businesses charge (in all cases) whatever price they think will make them the most money. That is what businesses do in a free market system.
That is not to say that the phenomenon that you are talking about does not exist. Firms do at times raise their prices steeply after disasters. This is done because they (like all firms) want to make the maximum profit and they believe they can do so by increasing prices.
One reason they believe this because of the idea of price elasticity of demand. Price elasticity of demand is a measure of what consumers do when the price of a certain good goes up. Consumers will still buy that good if it is a necessity and its purchase cannot be put off. Some things become immediate necessities after disasters. These include things like boards to board up houses or generators to produce electricity. Since people need these things immediately, they are willing to pay high prices.
In some cases, price increases come about because of reduced supply as well. If there is a storm and gasoline supplies are cut off, the supply of gasoline is reduced. People are more willing to pay a lot for what gas remains and gas stations can "price gouge."
In short, firms "price gouge" in the wake of disasters because firms in free markets tend to charge whatever price will give them the greatest amount of profit.