Imagine you are talking with another person, you ramble about models here and there, and suddenly in the middle of the conversation a question falls like thunder, freezing the discussion for a few seconds: “you are talking about models, what is a model?”. The word become so common nowadays that such a question might seem a menace for the conversation. You might remember then some of the dictionary definitions you heard so often, though they pull with them other terms that need further clarification. Some well-known approximate quotations on models might spring into your thinking process, though they don’t seem of any help now. The seconds pass and the time of silence looks like an eternity, while your interlocutor stares at you waiting for an answer. Unless you are prepared to give a definition on interlocutor’s understanding, you’ll more likely be in the chase of a such definition. Words and ideas succeed fast, the silence grows deeper, your interlocutor becomes more anxious, and is waiting for an answer.
What is a Model?
The easiest way to tackle such concepts is to start with a common representative example that can be used as scaffolding for a definition. If few people heard of “role models”, more likely almost all people having a TV, PC or similar device have heard of “top models” or “fashion models”. The “fashion model” as well the “role model” are idealized types of people, the first type considering mainly the appearance characteristics that makes a person attractive for presenting fashion, while the second considers mainly the characteristics that other people would want to copy. Both categories represent some idealizations in which some characteristics, qualities or features are evidenced.
When one speaks about fashion models one can easily come with some names of such models who were en vogue over the years. On the other side maybe for many will be more difficult to come with names of people who can be considered as role models, unless they had in their life people who functioned as role models. A “role model” seems to be more abstract as concept than the “fashion model”, as the physical qualities are easier to grasps then the inner qualities. There can be defined qualities like success, confidence, hardworking or sociability that are attributed to both roles. In fact the qualities of the two concepts can intertwine to the degree that for some people a fashion model and role model may be defined by the same qualities, or the differences are so small that they can be ignored.
Based on the two examples we can construct now a definition. Let’s consider a model as an idealization of a concrete or abstract object, in which some characteristics, qualities or features are considered as important and definitory.
The definition seems to be concise, clear, objective and precise, as much such a definition can be, so it looks like a good definition one can work with. The question is whether the praxis might invalidate it, where the gap between it and other definitions from technical literature is so big that makes this definition unusable. At least the following definitions seem to accord:
“A model is a simplification of reality intended to promote understanding.” 
“Models are replicas or representations of particular aspects and segments of the real world.” 
“A model is a representation of reality intended for some definite purpose .”.
“A model is an imitation of reality.” 
“A model is a representation of some subject matter.” 
From my point of view all these definitions aren’t good definitions because by attempting to be too general they lack precision. Is it any representation of some subject, of reality or part of it a model? Probably not! This raises another question: what isn’t a model? Unfortunately the answer isn’t that simple. Not any representation of something can be considered a model. Is it for example a cubistic representation of an object a model? The answer is again no! The model needs to keep certain characteristics of the object intended to represent, though more about it in other posts.
Here are a few other alternative definitions for models:
”A model is a physical, mathematical, or logical representation of a system entity, phenomenon, or process.” 
“model: the artificial object which explains all the empirical facts under consideration” 
Models in Context
Depending on the context in which is used, the concept of model is more elaborated and adapted as needed. One can talk about business, conceptual/thinking, mental, mathematical, statistical, scientific, mechanistic, behavioral, structural, social, political, logical, data or diagrammatic models. In fact models are the cornerstone of all sciences and pseudo-sciences, the foundation on which our understanding and knowledge is based upon. From the inner to the outer world, from simple to complex activities, from mathematics to religion, we use models on a daily basis. We think in models, or at least we use models in our thinking even if we are not aware of it.
From the literature reviewed over the years it can be observed that most of the definitions converge within the same boundaries, the difference residing mainly in the vocabulary used – idealization and characteristics being replaced by the family of words from the below table:
In various sources the denomination of model is substituted with synonyms that make better appeal of people’s understanding: pattern, example, emulation, analogy, visualization, system, replica, mold, mock-up, sketch, prototype, wireframe, schema, blueprint, (visual) aid, image (also picture, depiction), map, theory, principle, approximation, representation, allegory, metaphor, archetype, etc. All these can be considered upon context models, even if they might refer to totally different things.
Even if our thinking became more complex, the average individual juggling with increasingly abstract concepts, it seems that we fail to define basic concepts like the one of model. Starting from two examples I attempted to provide a good definition one can work with. I tried also to provide a mechanism that can be used to extrapolate definitions for similar concepts.
 SystemsThinking.org (2004) Models, by Gene Bellinger http://www.systems-thinking.org/simulation/model.htm
 Data Modeling Fundamentals: A Practical Guide for IT Professionals, by Paulraj Ponniah, John Wiley & Sons, ISBN: 978-0-471-79049-5, 2007
 Tools for Thinking: Modelling in Management Science, 3rd Ed., by Michael Pidd, John Wiley & Sons, ISBN-13: 978-0470721421, 2009
 Process Systems Engineering: Process Modelling and Model Analysis Vol. IV, by Ian T. Cameron, Katalin M Hangos, Academic Press, ISBN-13: 978-0121569310, 2001
 Workflow Modeling: Tools for Process Improvement and Applications Development, 2nd Ed, by Alec Sharp Patrick McDermott. Artech House, ISBN-13: 978-1-59693-192-3, 2009
 Systems Engineering Fundamentals. Defense Acquisition University Press, 2001
 The Concept of Model: An Introduction to the Materialist Epistemology of Mathematics, by Alain Badiou, re.press, ISBN-13: 978-0980305234, 2007