Application Management is one of the three primary ITIL functions that are defined in the Service Operation volume of the new ITIL v3.
A function is a concept that can be used to describe a collective of people, process and tools that carry out a specific activity, task or process.
Application Management as a function is responsible for daily operational activities related to in use applications. Application Management provides the in depth support and knowledge regarding any applications in use by the organization (purchased or developed in house).
The primary reason an application management function exists is to support business processes by understanding the requirements of applications and then to assist in the design and deployment and on-going support of these.
The Application Management function is not to be confused with Application Development, although there is often an overlap of the two.