Microservices are an architectural style where each service is implemented as an independent system. They can use their own persistence system (although it is not mandatory), deployment, language, ..
Because a system is composed by more than one service, each service will communicate with other services, typically using a lightweight protocol like HTTP and following a Restful Web approach. You can read more about microservices here:http://martinfowler.com/articles/microservices.html
Let's see a really simple example. Suppose we have a booking shop where users can navigate through a catalog and when they find a book which they want to see more information, they click on the isbn, and then a new screen is opened with detailed information of the book and comments about it written by readers.