Software program that performs a specific function directly for a user and can be executed without access to system control, monitoring, or administrative privileges.

 Source: DRI

A hardware/software system implemented to satisfy a particular set of requirements. In this context, an application incorporates a system used to satisfy a subset of requirements related to the verification or identification of an end user’s identity so that the end user’s identifier can be used to facilitate the end user’s interaction with the system.

 Source: NIST FIPS 201-3

Merriam-Webster Online Dictionary
application (noun)
an act of - applying
a) (1) an act of putting to use - application of new techniques
(2) a use to which something is put - new applications for old remedies
(3) a program (as a word processor or a spreadsheet) that performs one of the major tasks for which a computer is used
b) an act of administering or superposing - application of paint to a house
c) assiduous attention - succeeds by application to her studies
a) - request petition an application for financial aid
b) a form used in making a request
the practical inference to be derived from a discourse (as a moral tale)
a medicated or protective layer or material - an oily application for dry skin
capacity for practical use - words of varied application
Merriam-Webster Online Thesaurus
application (noun)
the act or practice of employing something for a particular purpose
application, employment, exercise, operation, play, usage
exertion; reuse
disuse, nonuse
An application is a computer program or set of programs designed to perform specific tasks for a user or a system. Examples of applications include web browsers, word processors, media players, and games.