I cannot understand why Wittgenstein's considerations about rule-following had such a large impact in many areas of philosophy. May you explain it to me?

This is a very good question. But there are several layers of answers, depending upon the question is asked from the point of view of the sociology of philosophy, the point of view of the history of it, or from the point of view of the intrinsic interest of a philosophical problem. If you question is about the latter, one can discern in it the following , fairly sceptical, one: why such a tiny, trivial sounding issue, dealing with such obvious facts as that people follow rules, can have become such an industry of ink spilling within the philosophical community for so many years? With respect ot the sociological/ historical setting, it seems that W and although I am not an expert of the history of Wittgenstein scholarship and Wittgenstein reception, ittgenstein's "rule-following" considerations have started during the 1970, when a number of philosophers have ceased to concentrate , when reading Wittgenstein, upon the private language problem or family ressemblances, and started to...