''Derived from the Webopedia[1] ...''

Infrastructure that handles requests for shared applications, processing and dispatching those requests.  For example, requests might arrive from web browsers, or web-services clients.  The application server receives the requests, and potentially activates application logic to handle the requests.  The logic itself may connect to a company's back-end business applications or databases, or to partner systems.  Because each different back-end system responds to its own, optimized set of network protocols (database access protocols, or message queue protocols, or protocols for accessing packaged applications, and so on), the application server works as a translator or bridge, allowing, for example, a customer with a browser to search an online retailer's database for pricing information and place orders.  Application servers are seen as filling a large and growing market; more than 25 companies now offer such application server products, and application server function is built-in to popular operating systems like MicrosoftWindowsServer.

See: 
* AtgDynamo
* WebLogic
* WebSphere
* SuniPlanet
* Iona
* BlueStone
* ZopeApplicationServer
* GemStone
* WebObjects
* ApacheTomcat
* WebridgeSuite
* ArsDigitaCommunitySystem
* CauchoResin
* QuiXote

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''I'd disagree with the "mid-sized" comment.  There's nothing about an app server that prevents it from being run on a single PC type machine for a very small business; or a distributed cluster of PC type machines for a large business; or even a mainframe.''

See: N-TierDesign