Giuseppe Mazzini was an Italian revolutionary. His most important accomplishment was helping Italy become a united country.
Between the fall of the Roman Empire and the middle 1800s, Italy had never been a unified country. It had been made up of various city-states and small countries. Parts of what is now Italy had been controlled by France or Austria. The result was severe fragmentation of people that we would now call Italian.
In the early 1800s, Italians started to become more nationalistic. Mazzini, who was born in 1805, was part of this movement. He was one of its main intellectual leaders, calling for both Italian unity and for a republican form of government rather than a monarchy. In 1848, forces from this movement were able to eject the pope from Rome (which was then the capital of the Papal States) and set up a republic with Mazzini as its leader. This republic did not last long, but it was a major stepping-stone on the road to Italian unification.
Italian unification was eventually accomplished by people other than Mazzini who created a kingdom rather than a republic. Mazzini was very unhappy with this, but at least he had accomplished something; he had helped to bring about Italian unification.