Application Server:

An application server is a server program in a computer in a distributed network that provides the business logic for an application program. The application server is frequently viewed as part of a three-tier application, consisting of a graphical user interface (GUI) server, an application (business logic) server, and a database and transaction server. More descriptively, it can be viewed as dividing an application into:
A first-tier, front-end, Web browser-based graphical user interface, usually at a personal computer or workstation
A middle-tier business logic application or set of applications, possibly on a local area network or intranet server
A third-tier, back-end, database and transaction server, sometimes on a mainframe or large server