Rivalry in economics means that when more than one person or company offer similar products, they compete with each other to get more customers. It's like when you and your friends have a race to see who can run the fastest, everyone tries to beat each other to win. In the same way, companies try to beat each other by offering better products, lower prices or more services to their customers.
This competition can be good for the customers because it gives them more options to choose from, and companies have to work harder to make their products better to satisfy their customers. However, it can be bad for the companies because they may have to lower their prices to compete or go out of business.
For example, if there are two pizza shops in your neighborhood, they both offer pizza, but they compete with each other to make better pizza, offer more toppings, or offer it at a lower price to get more customers. They are rivals because they are in competition with each other.