It is important to note that India, prior to the Great Rebellion, was governed and controlled by the British East India Company rather than Great Britain itself. To consolidate Company control over India, the Company used Indian troops to defend their interests. These soldiers formed the backbone of the East India Company's own military forces, and they were the troops who mutinied, starting the Rebellion.
As has already been addressed, there were already tensions within Company-ruled India, and these tensions were inflamed by rumors of rifle cartridges greased with animal parts. These rumors led to a number of confrontations between sepoys and their officers, which culminated with the mutiny at Meerut. Knowledge of these events inspired similar acts of rebellion, and thus the unrest spread.
The Great Rebellion began with the sepoys and spread toward other disaffected portions of the Indian population, such as peasants and local political elites. Thus, the rebellion's scope grew larger than the soldier class which launched it. In the end, the British government itself intervened to quash the revolt.