A Project is a logical separation for work within Cloud CMS. It could be a site, a sub-site, a department, a web project or anything else you'd like. Projects let you organize teams, invite members and provide a place for you to collaborate on content.
An Application is something that you create to provision resources and services dedicated to your web site or web/mobile application. Each Application provides storage and services that your app can access for things like user registration, password recovery and user settings retrieval.
One way to think of it is that Projects are business-side places where content is worked on and approved. Applications are delivery-side places focused on end users and presentation. Applications can draw content from a single Project or from multiple Projects.
Applications also give you a place to provide additional details such as GitHub source URLs so that Cloud CMS can automatically handle the deployment and hosting of your apps.