Price elasticity of product demand is measuring the relation of price and demand for the product. The price variation is influencing product demand in different ways. As a general rule the price increase is causing demand decrease.

But this general rule has several different situations. The demand does not change at the same proportion for every product. Some product are more sensitive, while some other are les sensitive. The life necessary commodities are usually less sensitive, meaning that the demand will change at the smaller rate than the price. The luxury products or products that can be substituted are changing at the greater rate than the priice change. This relation of price and demand is called price elasticity of demand. 

Relatively Inelastic Demand is the situation when price ( p ) change does not change the demand ( q ) at the same rate. If the price increase for certain percentage, the demand will be reduced but only for the smaller percentage. Also, if the price decrease, the demand will not go up for the same percentage. The life necessary product like food or clothing are characterized by this elasticity of demand model.
Perfectly Inelastic Demand is more the theoretical extreme, but the core products, like bread or water have demand elasticity approximate to this model. no matter what is the price of bread you will still need it.
Relatively Elastic Demand is the situation when price change at the certain percentage is causing change in demand of even greater percentage. The relatively inelastic demand is typical for luxury products. In the period of reduced income people try to cut travels, luxury products and unnecessary spending. When the income is increased the consumers are buying more luxury goods.
Perfectly Elastic Demand special example of price elasticity when any change of price is reducing demand to zero.

Another elasticity model is the unit ( unitary ) elasticity. This elasticity model is descripting the situation when the change of price of X percentage is causing the X percentage change of demand. This apply to both situation, the price increase and price decrease.