Huh, I am not exactly sure if the premise of your question is correct. To my knowledge only the unification of West and East Germany in 1990 is commonly referred to as "re-unification". Perhaps you could specify where you heard or read that?

I suspect, what you might be on to is what is often called the unification of Germany: the foundation of the German Empire by a number of German states (excl. Austria) under the guide of Prussia in 1871. The Empire was the first modern German nation state, so one might say this was the first German "unification".

To call 1871 a *re-*unification however would be a bit of a stretch as nationality is a modern concept and there was no political entity before that could claim to be a German state in the modern sense. Nevertheless, the German Empire was sometimes called the Second Reich to provide a sense of continuity with the Holy Roman Empire of the Medieval and Early Modern Era. (Ever wonder where the term Third Reich came from?) You see, while nationalism is a profoundly modern conception it still reaches out into the past to construct a pre-modern lineage, looking for previous incarnations of its nation in former states encompassing the same regions, speaking same or similar languages etc. This way, people could be referring to a unification as a re-unification if they chose to believe that in the relevant case things grow together which already belong together anyway.