The answer to this can be neatly summed up by one line from Guns, Germs, and Steel. On the bottom of p. 258 in my edition of the book (about 4 pages from the end of the chapter), Diamond says "...technology begets more technology." This is why farming's autocatalytic nature matters.
When a society starts to farm, it needs various technologies. As it invents those, they lead to other technologies. Soon, the farming society has all sorts of technologies that have branched off from one another. Meanwhile, a society that did not start farming, has no technology. It never invented the first set of technololgy that "begat" all the other technologies. Because it never invented the farm-related technology, it could not autocatalyze and create more technologies. This means that, over time, the non-farming society falls farther and farther behind the farming society in terms of technology.
Because one technology leads to more and more technology (because farming is autocatalytic), societies can develop huge disparities in term so their technological levels.