Public cloud service is used when the application is used by lots of people like email service or say the organization is providing software as a service for the users or there is some collaborative project going on within the organization. Basically this type of service is a good example of economies of scale and it is inexpensive to setup too.
A simple everyday example of public cloud service would be email and file sharing and storage services like Google dropbox where people can store their files instead of storing it to their personal computer. For business applications Amazon EC2, IBM’s Blue, Google App Engine, Microsoft Azure service platform etc. are few examples of public cloud service. These service providers operate on pay per use model. This type of solution requires little setup cost and hence provides a cost effective solution to many organizations.