Introduction:Any subject matter when defined to explain what exactly it is, we may find one definition. Always a definition explains what that particular subject matter is. The subject operation researchis a branch of mathematics  specially applied mathematics, used to provide a scientific base for management to take timely and effective decisions to their problems.
Definitions:
Important definitions are discussed below.
Operations Research is the art of winning wars without actually fighting. – Aurther Clarke.
Operations Research is the art of giving bad answers to problems where otherwise worse answers are given.  T.L. Satty.
Operations Research is Research into Operations.  J. Steinhardt.

This definition does not throw any light on the subject matter, but it is oriented towards warfare.

It means to say that the directions for fighting are planned and guidance is given from remote area, according to which the war is fought and won.

This definition covers one aspect of decisionmaking, i.e., choosing the best alternative among the list of available alternatives. It says that if the decisions are made on guesswork, we may face the worse situation. But if the decisions are made on scientific basis, it will help us to make better decisions.

This definition does not give anything in clear about the subject of Operations Research and simply says that it is research in to operations.

Operationsmay here be referred as military activities or simply the operations that an executive performs in his organisation while taking decisions.

Researchin the word means that finding a new approach
Operations Research is defined as Scientific method for providing executive departments a quantitative basis for decisions regarding the operations under their control.  P.M. Morse and G.E. Kimball.
Operations Research is study of administrative system pursued in the same scientific manner in which system in Physics, Chemistry and Biology are studied in natural sciences.
Operations Research is the application of scientific methods, techniques and tools to operation of a system with optimum solution to the problem.  Churchman, Ackoff and Arnoff.
Operations Research is the application of the theories of Probability, Statistics, Queuing, Games, Linear Programming etc., to the problems of War, Government and Industry.
Operations Research is the use of Scientific Methods to provide criteria or decisions regarding manmachine systems involving repetitive operations.
Operations Research is applied decision theory. It uses any scientific, mathematical or logical means to attempt to cope with problems that confront the executive, when he tries to achieve a thorough going rationally in dealing with his decision problem.  D.W. Miller and M.K. Starr.

This definition suggests that the Operations Research provides scientific methods for an executive to make optimal decisions. But does not give any information about various models or methods. But this suggests that executives can use scientific methods for decisionmaking.

This definition is more elaborate than the above given definitions.

It clearly directs that Operations Research can also be considered as applied science and before the course of action is decided, the alternatives available are subjected to scientific analysis and optimal alternative is selected.

This definition clearly states that the operations research applies scientific methods to find an optimum solution to the problem of a system. A system may be a production system or information system or any system, which involves men, machine and other resources.

This definition gives a list of various techniques used in Operations Research by various managers to solve the problems under their control.

This definition talks about man machine system and use of scientific methods and decision making.It is more general and comprehensive and exhaustive than other definitions. Wherevera study of system involving man and machine, the person in charge of the system andinvolved in decisionmaking will use scientific methods to make optimal decisions.

This definition also explains that operations research uses scientific methods or logical means for getting solutions to the executive problems. It too does not give the characteristics of Operations Research
But salient features of above said definitions are:

Operations Research uses Scientific Methods for making decisions.

It is interdisciplinary approach for solving problems and it uses the knowledge and experience of experts in various fields.

While analyzing the problems all aspects are considered and examined and analyzed scientifically for finding the optimal solution for the problem on hand.
As operations research has scientific approach, it improves the quality of answers to the problems