In metaphysics, extension signifies both 'stretching out' (Latin: extensio) as well as later 'taking up space', and most recently, spreading one's internal mental cognition into the external world.
The history of thinking about extension can be traced back at least to Archytas' spear analogy for the infinity of space. How far can one's hand or spear stretch out until it reaches the edge of reality? "If I arrived at the outermost edge of the heaven, could I extend my hand or staff into what is outside or not? It would be paradoxical [given our normal assumptions about the nature of space] not to be able to extend it."
History
Descartes
René Descartes defined extension as the property of existing in more than one dimension, a property that was later followed up in Grassmann's n-dimensional algebra. For Descartes, the primary characteristic of matter is extension (res extensa), just as the primary characteristic of mind is thought (res cogitans).
Newton
After rejecting Cartesian identification of body with extension, Newton turns to the question of what the nature of the "immobile being"—space or extension itself, distinguished from body—was. He raises three possible definitions for extension: as a kind of substance; or as a kind of accident (a standard philosophical term for attribute: anything that can be predicated of substance); or "simply nothing" (a reference to atomism), all of which he repudiates. Instead he proposes that extension "has a certain mode of existence of its own, which agrees neither with substances nor accidents." After struggling with this question, Newton provides perhaps one of the clearest definitions of extension