A firm uses public relations to promote its image so that it can have a better chance of selling its product. It is trying to create demand for its product.
One of the major determinants of demand for many products is consumer tastes. Consumers buy things that make them feel good about themselves. One thing that helps them to feel this way is to buy from a company that has a good public image. Most people do not want to buy their clothes, for example, from a company that has a terrible reputation for mistreating its workers. They would not feel proud of their clothes if they did. People want to buy things from companies that are "good guys."
This is why firms pay for public relations. They want to convince the public that they are honorable companies that people should want to associate themselves with. This will lead to better sales for the firm.