Price elasticity of demand has to do with the extent to which the quantity demanded of a product will change as the price of that product changes. The more the quantity demanded changes in response to price, the more elastic the demand for the product is.
One example of this might be the demand for gasoline. As the price of gasoline rises, the quantity demanded of gasoline drops, but it does not drop by a great deal. This is because gasoline is fairly necessary for people's every day lives. Therefore, the demand for gas is relatively inelastic.
By contrast, the demand for something like red t-shirts would be quite elastic. If the price of red t-shirts went up by a great deal, people would simply switch to wearing some other color of shirt. The demand for red t-shirts is relatively elastic because there are many substitutes for red t-shirts.