University of Alberta Dictionary of Cognitive Science: Extension

The extension of a term in the class of things in the world that the term "picks out" (i.e., that the term distinguishes from other entities in the world). For example, the extension of the term "green" is the set of green things in the world.

A term's extension -- the class to which it refers is distinct from its intension, which is all of the psychological associations that one has with that term. For instance, the extension of the term 'cat' is all the cats; the intension of the term is related to your experience of cats, their history, their attributes, etc.

The notion of extension, and its distinction from intension, is enormously important in the philosophy of language. For instance, Putnam's (1973, 1988) famous twin earth thought experiment was designed to demonstrate the possibility that two terms could have the same intension, but have different extensions. In Putnam's example, water on Earth has the composition H₂0, but on Twin Earth has the composition XYZ. Otherwise, the two different kinds of water are identical. As a result, our experiences (and therefore intensions) of water in either world would be identical. However, the extension of the term 'water' on Earth would differ from the extension of the term 'water' on Twin Earth. This raises the possibility that "meaning ain't in the head".

References:

Putnam, H. (1973). Meaning and reference," Journal of Philosophy 70, 699-711.
Putnam, H. (1988). Representation And Reality. Cambridge, MA: MIT Press.

(Revised March 2010