Representation is a technique that is necessary in any system that process real-world signals or any other sort of information. In your brain, the firing rate of a particular neuron is your mind's representation of the temperature of a certain tiny spot on your left index finger. In language we make use of sounds or signs to communicate aspects of our thoughts. But a system doesn't have to have anything even vaguely resembling a mind in order to exploit representation. Notably, all known life uses DNA represent the structure of proteins. Likewise, in your house's digital thermostat, a certain register represents the current temperature (68) as a binary integer 10000100, and these bits are in turn represented by electronic signals.
Representation is ever-present, but it often proves difficult to pin down just what we mean by representation. Semiotics is one effort to systematically study representation and related concepts (symbol, sign), but the results often seem obscure. We suffer from the dual problem that representation (in the form of language) is natural and effortless, but some meta-representation (Story) is also a necessary part of any study of representation. This creates vast potential for Level Confusion. The representations that make up our own minds are also completely inaccessible to conscious awareness (see The User Interface Analogy), inclining us to Naive Realism and Mind/Body Dualism. It is like a fish studying water.
The field that has had far more impact on our understanding of representation and symbol is Computer Science, especially in the sub-disciplines Artificial Intelligence, Machine Learning and Digital Signal Processing. See also Representational Opacity.