The essence of the answer to your question is that the average German would have felt intense pride in this unification, because all of a sudden he was part of one of the mightiest nation-states in the world. It all happened in less than a decade too. Prussia went from the weakest of the five Great Powers in 1862, after Austria, Britain, France and Russia, to the most powerful state in Europe. Other states that joined Prussia went from diplomatic nobodies to the status of a superpower. Moreover, two of the Great Powers were beaten in the process, first Austria and later France, the latter of which was especially satisfying because of the humiliating Napoleonic campaigns half a century earlier. Napoleon marched straight through the heartland of what would later become Germany.

All this should be understood against the background of the intense nationalism in Europe at the time. The Franco-Prussian War, the final act of the German unification process, released a surge of patriotism in Germany. Winning the war, completing the unification and becoming the greatest power in Europe all added to a general feeling of pride and the conviction that they were the best of the European species.

Source:

An older Dutch book and my first year handbook 'A History of Modern Western Society' by McKay et al.

Depends on whether you mean the unification of 1871 or re-the unification of 1990, I guess.