It followed Poland's first free post-war elections in May of that year and the cutting of barbed wire along the Hungarian-Austrian border in summer. In August, large numbers of East Germans camped out near Lake Balaton, a resort and spa area in the west of Hungary. It was so common for East Bloc denizens (as well as Austrians and Germans) to vacation there, it didn't really even look all that suspicious, but they were biding their time, having heard rumors of border openings. As Deutsche Welle notes in recent reportage, many of the locals told them which lookout towers were likely to go unused.
The breakthrough was the Pan-European Picnic, in the woods near Sopron, Hungary, an event co-sponsored by Otto von Habsburg, the last crown prince of Austria-Hungary, and reform-minded Communist parliamentarian Imre Pozsgay. There were rumors, once again, of a border opening: according to the Deutsche Welle article, Hungarian guards checked the documents of Austrian citizens, while ignoring the East Germans pouring through into Austria - about 700 in number.
More and more "Ossies" attempted the escape into Austria, and in September many others went to Prague - entering West German territory by jumping the fence into the embassy compound. These are the people Genscher is addressing.
The Pan-European Picnic and the events at the Prague Embassy were two crucial leadups to the Fall of the Berlin Wall.