A model is a simplified representation of a system or phenomenon with any hypotheses required to describe the system or explain the phenomenon, often mathematically. It is an abstraction of reality emphasizing those aspects that are of interest to someone [ISERN]
A model is a coherent set of formal elements describing something (e.g., a system, bank, phone or a train) built for some purpose that is amenable to a particular form of analysis, such as: communication of ideas between people and machines, completeness checking, race condition analysis, test case generation, viability in terms of indicators such as cost and estimation, standards, transformation into an implementation. [MCF2003]
Modeling, in the broadest sense, is the cost-effective use of something in place of something else for some cognitive purpose. It allows us to use something that is simpler, safer, or cheaper than reality instead of reality for some purpose.
A model represents reality for the given purpose; the model is an abstraction of reality in the sense that it cannot represent all aspects or reality. This allows us to deal with the world in a simplified manner, avoiding the complexity, danger and irreversibility of reality.
Jeff Rothenberg