To reach further than before. Extension adds to what is there rather than replacing it.
Latin extendere, ex- (out) plus tendere (to stretch); the verb travelled from the literal stretching of a physical thing, a rope or a limb, to the more general reaching of anything, space, time, or a plan, beyond where it had stood before.
Its root is the same stretch that gives tendon and tension: a rope pulled longer without being cut. What extends reaches further along the line it already was, and stays whole the entire way.