c.1400, from Old French extension (14c.) and directly from Latin extensionem/extentionem (nominative extensio/extentio), noun of action from past participle stem of extendere (see extend). In a concrete sense, "extended portion of something" (a railroad, etc.), from 1852. Telephone sense is from 1906.
extension ex·ten·sion (ĭk-stěn'shən)
The act of straightening or extending a flexed limb.
A pulling or dragging force exerted on a limb in a distal direction.
Extensional properties, e.g. extensional equality, relate to the "black-box" behaviour of an object, i.e. how its output depends on its input. The opposite is intensional which concerns how the object is implemented.