A hosted application is a software as a service (SaaS) solution that allows users to execute and operate a software application entirely from the cloud on a recurring subscription.
Hosted applications are hosted and powered from the remote cloud infrastructure and are accessed globally through the Internet. They provide the same functionality as locally installed software but can be updated more easily.
Hosted applications may also be known as Internet-based applications, Web applications and online applications, although these terms often have a larger scope.
Techopedia explains Hosted Application
Hosted applications are among the pioneer service model of cloud services, allowing users to receive a similar application functionality experience through their Web browsers as they would with desktop applications. Hosted applications are deployed easily compared to conventional software as they require no upfront installation and have minimal integration requirements. Because they are designed to be accessed through Web browsers and operating systems, they pose a low risk of local system corruption.
Hosted applications being managed by the service provider are routinely updated and patched with the most stable version and is backed by continual technical and customer support. Although most hosted application offerings don't require a client-end installation, some require a thin client application to be installed at a local workstation for accessing the remote application.