The decline of Austria in the 1850s helped Piedmont (led by Count Camillo Cavour) gain control of most of Italy because Austria had been the major power in Italy. As it weakened, it became more possible for Piedmont to gain strength and eventually to oust Austria from the peninsula.
At the Congress of Vienna in 1814 and 1815, Austria was put in a position of power in Italy. It directly controlled two major territories in the north, Lombardy and Venetia. It was by far the greatest power on the Italian peninsula and it used its power to indirectly control most of the other states that were created in Italy at that time. For example, there was a revolution in Piedmont in the early 1820s that overthrew their monarchy and created a republic. Austria did not like this and used military force to restore the monarchy.
In such a situation, it would have been hard for Piedmont to grow stronger and for it to take control of Italy. However, things changed. Austria started to become weaker. This allowed a strong leader like Cavour to become important in Piedmont. Austrian weakness, along with French help, changed the balance of power on the peninsula. Because of this, Cavour and his forces were able to take power over most of Italy by the early 1860s.