Louis Mountbatten played a role in the independence of India because he was the last viceroy appointed by the British crown to govern India. He was sent to India with the explicit task of transferring power from Britain to an independent Indian government.
Mountbatten played two major roles in this process. First of all, he managed to help the cause of Indian unity by persuading the Princely States not to pursue independence or power. These states had sworn allegiance to Britain and had been independent before they did so. Mountbatten persuaded them to renounce any claims to independence. By doing this, he helped unify the country.
Conversely, Mountbatten also helped to cause the split between India and what is now Pakistan (and Bangladesh). He was quick to support the idea of partition and the plan that laid out the boundaries of the two (now three) nations bears his name. He is blamed by some for the bloodshed that resulted.