Italy became united as a kingdom in 1861 under Victor Emmanuel II. Prior to that, this king had been the king of Sardinia. Aided by the Count of Cavour, Victor Emmanuel succeeded in uniting most of the country. Italian unification continued with the acquisition of Venice in 1866; Italy had fought with Prussia against Austria and was rewarded. Then the Papal States were absorbed in 1870. With Italian unification completed, Rome became the capital in 1871.
There were many Italians who remained dissatisfied with the new nation's geographic scope, however. Their movement was known as Italia irredenta (unredeemed Italy). These nationalists coveted additional lands in Austria. Italy's desire for these additional territories was the main reason for its entry into World War I.
Italy faced the Roman Question after 1871 because the papacy did not accept the loss of its lands. This created a problem, because the vast majority of Italians were Roman Catholic. The standoff between Italy and the papacy dragged on for nearly sixty years. Finally, the Lateran Treaty of 1929 settled the controversy.
The new nation had economic problems and faced numerous difficulties. Italy struggled with land reform. Many Italians emigrated to the Americas. The 1890s were especially difficult, as the nation faced riots at home and military defeat in Africa at Adowa (1896). In 1900, Italy's king was assassinated by anarchists.
After unification, foreign powers could no longer colonize parts of the Italian Peninsula as they had done for centuries. But the new nation was not a great power and it was hobbled by its many problems. Its instability and losses in World War I enabled Benito Mussolini to become dictator in the 1920s.
From a purely political perspective, Italian unification greatly affected the balance of European politics. Unification represented a dramatic increase in Italian power, as well as a significant loss to Austria (which had previously controlled much of Northern Italy). At the same time, you should consider that these changes were not entirely welcomed by a great many Italians.
As historian John Merriman shows in A History of Modern Europe (3rd Edition), Italy actually remained deeply divided in social matters and internal politics, with a significant number of Italians continuing to retain primary loyalties to their localities and the Church. Indeed, this fractal quality is reflected in patterns of language. Merriman writes:
Almost 70 percent of the population was illiterate in 1871 and 50 percent in 1900, even though the peninsula now shared a common written Italian language. In 1860, almost 98 percent of the population spoke dialects in daily life and not Italian. Schoolteachers sent to Sicily from the north were taken for Englishmen. (657-658)
As if this was not enough, also remember that Italian unification came at the expense of the Papacy, which resulted in a great deal of hostility for the new government by the Church (and remember: the Church still wielded a great deal of influence and religious authority in Italy at the time).
The Italian government was largely dominated by northern Italy, and many southern Italians looked upon it with distrust. Here, Merriman writes:
"Italy" was seen as a northern ploy to bilk money through taxes, or to draft the sons of southern Italians into the army, or to undercut what seemed to be legitimate local influence and ways of doing things (658)
Even after unification, Italy remained a deeply divided country.
Despite these internal divisions (and perhaps even because of them), the Italian nation state would exhibit a militaristic nationalism in the years that would follow. (You can see the long term presence of this militaristic nationalism with Italy's entry into World War I and, later still, the regime of Mussolini.)
Prior to unification, the Italian peninsula was made up of a consortium of fragmented states which were conquered and rebuilt as republics by the French but were later vanquished by the Russian and Austrian armies. The first development of republics in these disjointed states introduced the idea of a government and society that provided freedom and equality. This revolution instilled in the populace the need to focus on nationalism. This growing sense of nationalism led to the eventual unification. The Italian Unification earned Italy its independence and built its capacity to influence regional politics. Italy as a unified state had the capacity to build its armies to protect its sovereignty. A unified Italy developed its ability and capacity to trade with other nations and even build relations with nations such as the United States who offered citizenship and immigration opportunities.
A unified Italy, along with Germany, which unified a few years later, permanently altered the strategic dynamic on continental Europe. On the one hand, Italy never became the dominant military power that Germany, unfied under Prussia, did. But on the other, Italy posed a threat on Austria-Hungary's southern flank, and its independence ended hundreds of years of French involvement with the politics on the peninsula. Though they fought unification on the battlefields, Austria almost immediately made overtures to Italy, who joined them in the Triple Alliance in 1882. The unification preceded a degree of cultural unity, as regions of the nation that previously had almost nothing in common with each other found themselves under the same political head.