The accepted definition of Application Service Provider (ASP) is any company that hosts and manages applications over the Internet (or WAN) for multiple customers.
Cloud Computing is a model used by ASPs to host applications for clients and provide services over the internet. It includes hosted applications and also virtual information technology services like virtual servers and operating systems.
Application Service Providers provide a new way of offering software. In the past, software was often licensed to clients and managed by the customer. ASP model is to rent such software over the internet and manage the software for the client. The client only pays for the amount of time they use the software service.
Many ASPs now focus on Software management and providing software-as-a-service which focuses on the service provided to the client rather than the specific software application itself. Therefore they may use several different application to provide a specific business process service to a client.
ASPs also do Application Hosting for other companies where they offer custom applications to businesses who access them over a secure portal.
Examples of software offered through application hosting may include desktop productivity suites and other high value software that take care of a specific business process like order processing, employee management, accounting or department like human resources, manufacturing, or supply chain management.
Big ASPs have developed Multi-application suites. These are usually industry specific but powerful software suites that provides all the functionalities that an organization may need. This saves them money because they don't have to build custom software for specific clients. They can sell them these Multi-Application suites that can do all imaginable functions in that particular industry.
ASPs also offer System management services like data backups, software upgrades and customization and hardware maintenance.
While many ASPs services are accessed via the public internet, many provide their services over private networks using high speed leased lines and fiber optics cables.