Running jobs on remote computers was one of the key goals of the funding for ARPANet, the network that preceded the Internet. ARPA wanted the researchers they funded to be able to run jobs on each other's computers.
Today, there are still companies providing complete applications as services on the Internet, but others offer components that can be used as part of a service.
For example, UPS provides a service that allows shipping customers to include tracking information on their Web sites.
The package tracking service is available only to large UPS customers, but other services are available to nearly everyone. For example, the following links lead to dynamic maps. Looking at the source code, you see that they are provided as a Web service running on a Google server.
Web services allow developers to add powerful capability with little effort. There may be a charge to use a service or it may be free. Organizations can also develop services for internal use, offering them on an intranet or extranet.