How does demand relate to price?
The higher the demand, the higher the price will be.
Keeping supply constant, if the demand for a good increases, its price will increase, since the consumers will start competing with each other for the good. This is directly linked to the scarcity law.
When it rains, one can expect that the price of umbrellas will increase. In the short run, the firms can't increase the production of umbrellas, so there will be less umbrellas available for each consumer. They will compete with each other and the companies will raise the prices, so that they can earn higher profits.
To see this, try drawing a graph with price in the vertical axis and quantities in the horizontal axis and a demand curve and a supply curve (in the shape of and X, to simplify). Then dislocate the demand curve to the right (symbolizing and increase in demand due to external reasons). You will see that the point where demand and supply intercept will be upper and more to the right, meaning that more quantities will be demanded and the price will go up.