Clearly, none of us is playing by the rules in this game, otherwise we would all concentrate on a few key inventions that are obviously the most important — the Indo-Arabic number system including zero, computers, the contraceptive pill. Instead we are all reading the suggestions so far and then trying to select something different. Because I've come in late my friend Nicholas Humphrey has bagged my first thought — reading glasses, so I'll break the rules in two ways by choosing something which was invented more than two thousand years ago but refined over the last two thousand years.
In fact I'll break the rules a third time by choosing two things — chairs and stairs. Apart from the fact that they rhyme, they also represent an imaginative leap by seeing the value to the human anatomy of an idealised platform in space at a certain height. A platform of, say, 7 inches would enable a person to raise himself towards some higher objective without undue effort, but that's as far as it goes.
But if, from that new starting point, a further platform of the same height could be constructed, the objective could be more closely approached. The refinements have all been to do with the fact that the greater the height you want to reach the larger the floor area that has to be taken up by the staircase. But landings and 180 degree turns helped to solve that problem, along with the even later improvement of a spiral structure.
The consequences of stairs have obviously included greater density of occupation of site areas, but they have also included the propagation of the Muslim religion by allowing muezzins to call the faithful to prayer from minarets. As far as chairs are concerned, the same thought process was involved — seeing the value of a platform at just above knee height and then constructing it.
Portability came in at some stage as well so that instead of finding somewhere — a wall, a rock, etc — of the right height you carry around with you, or position where you liked, the place to park your butt. Somehow, the height was chosen, or evolved, so that we can stay for the maximum time in a fixed position with eyes,hands and arms free to do what eyes, hands and arms are good at. Lying down, standing up, and squatting all get uncomfortable after a while, particularly for reading or writing (although we have to accept that medieval monks seemed to manage O.K, transcribing manuscripts standing up.)