My initial thought of how to define the importance of an invention was to imagine the impact which would be caused by its absence. But having just sat through yet another viewing of "Its A Wonderful Life," I am inspired to leave contemplation of the contingencies of history to others better suited to the task. And so, I will vote for my "knee-jerk" response: The Telescope.
The invention of the telescope and its subsequent refinement and use by Galileo marked the birth of the modern scientific method and set the stage for a dramatic reassessment of our place in the cosmos. A technological device revealed conclusively that there is so much more to the universe than is available to our unaided senses. And these revelations, in time, have established the unforeseen vastness of our dynamic, expanding universe, shown that our galaxy is but one among countless others, and introduced us to a wealth of exotic astrophysical structures.