Hi there, you might be interested in two answers I've written previously. One on unification in general and one on The Schleswig-Holstein question.

The wars leading up to unification were not strictly necessary, but they played a role in allowing Prussia to emerge as as the pre-eminent German state, and in ensuring that Germany would not be challenged when she did finally unify. The conflicts, both diplomatic and military, with Austria enabled Prussia to assume their leading role in German affairs. The war with France ensured that they did not pose a threat to a newly united Germany, and that other European nations knew that Germany was a serious military power. As I discuss in the first answer above, a major impetus for the wars was also the aggressive Foreign Policy of Bismarck, whose policy was to unite Germany, 'not by speeches and majority resolutions ... but by iron and blood.' Such an approach was undeniably effective.

@abrytan Gives a good succinct reasoning as to Prussia's position. I want to go more into the mindset of the Prussians during this period. After the Congress of Vienna in 1816 Prussia was left with territory scattered along the Rhine in the west and the Prussian traditional territories in the east. This meant that the Prussian Kingdom had a precarious military and cultural position, as the west Prussians did not culturally consider themselves Prussian. The Congress of Vienna established what was called colloquially called the Concert of Europe, whereby Austria, Russia, and France were the dominant powers, with Spain, Piedmont-Sardinia (Northern Italy), Naples, Bavaria, Saxony, Denmark, Sweden, and Prussia were the secondary powers. The Austrians acted as the European policemen, squelching revolts and ensuring that Europe remained more-or-less intact. The post-Napoleonic settlement left around 20 countries, duchies, and city states in the Germanies.

This balance of power existed up until the 1848 liberal revolutions that wracked most of continental Europe, and led to numerous governments reforming to become constitutional monarchies. In Austria the Hungarians rose up, and it was only with the aid of the Russians that Austria managed to suppress the rebellion. This led to a realisation that Austria was not as strong as the other European powers realised, but with the alignment with Russia there was little the other European powers could do. In France this revolution led to the rise of Louis Napoleon as emperor. In Prussia the King established a Prussian form of constitutional monarchy, which put the army in the hands of the king and above the parliament. One of the key outcomes of the 1848 revolutions was the fall of the Austrian Chancellor Metternich, who had orchestrated the Europe wide suppression of liberal rights.

In 1853 the Russians declared war on the Ottomans to seize control of Constantinople, with the French and British stepping into aid the Turks. Russia assumed that Austria would honour its obligations, especially in light of the 1848 intervention, but the Austrians did not feel in a position to fight a war with France, so decided to stay neutral. This angered the Russians to the point where they refused to help the Austrians again militarily, a point that the Prussians picked up on.

One of the consequences of the 1848 revolutions was that German pan-nationalism exploded in popular culture, especially in the northern Germanies. The pan-German movement looked for a country to lead the struggle for a unified Germany, and when Bismarck came to power in 1862 he tapped into this movement to position Prussia as the leading Germanic nation. While he thundered 'blood and iron', and certainly wielded the Prussian military to great effect, Bismarck's key insight was the fallibility of the continental system, the weaknesses of the nations around Prussia, and the astute understanding of how to work with the tools providence provided with him. He understood that to dislodge Austria from its key position of power in the Germanies he would need to use diplomacy, military ingenuity, and luck to achieve his ends. To this wit he and key Prussian ministers built and trained the Prussian military to fight short sharp wars with the latest technology, while at the same time cajoling the smaller Germanic diplomatically.

Prussia used the 1864 Schleswig war to lull Austria into a false sense of security and demonstrate its military capabilities. The Prussian and Austrian victory enabled the Prussians to diplomatically manoeuvre themselves into a position of strength to the point that when they declared war on Austria in 1866 they were able to win the war quickly and decisively. A key reason for their victory was Russia staying out of the war, and it meant that any future unified Germany would be on Prussian terms, not Austrian. In 1866 the North German Federation was created, with Prussia being the dominant player. The southern German states were still within Austria's sphere of influence, though after 1866 they gravitated more towards the north.

Between 1867 and 1870 Bismark negotiated defence treaties with Saxony, Wurttemburg, Bavaria, and Baden and other smaller independent German states. This meant that if the North German Confederation was attacked the southern German states were treaty bound to join in the Prussian defence. In 1870 Bismarck engineered a situation where demands made by the French ambassador to the King were leaked to the press, causing France to loose face and giving the French Emperor a casus belli to declare war. In 1870 the French army was regarded as the best in the world, so Louis Napoleon was confident that the French would win the war easily, and duly declared was on the North German Confederation. This declaration of war caused all the defensive treaties to be invoked by Bismarck, and after the Prussians defeated the French in the Franco-Prussian War Bismarck was now in a political position to declare the Second German Reich in 1871. Without the 1870 war there is a likelihood that the defence treaties would have faltered or crumbled, and Bismarck feared that the grand unifying scheme would be halted.

So, to answer your question. The three wars each served a different purpose, and as each was short and sharp enabled the Prussians to retain the core of trained troops without expending too much state capital or material in the process. Bismarck used war as an extension of diplomacy, and through judicious use of cunning, luck, and military prudence was able to craft a unified Germany out of the 20 or so states in 1860. Germany could easily have included Bohemia, Moravia, Austria, and other constituent parts of Austria has the politics, wars, and diplomacy worked out differently. So the reason why the wars were necessary was to speed up the unification processes in favour of Prussia, and quickly resolve situations that may have taken a generation to resolve.