The Sepoy Rebellion, also known as the Indian Mutiny of 1857-58, was very much the result of a clash of cultures. Since the 1820s, the British East India Company and other British presences in India had been pushing the tenets of Western Civilization on the subcontinent. They hoped to gain supremacy in part through dominating the political, social, cultural, and economic spheres of Indian society. As a result, they began usurping control from the traditional Hindu and Muslim principalities. This was especially the case once the Doctrine of Lapse was established in the late 1840s. This allowed the British to annex the land of any local ruler who died without a natural successor. This practice caused a great amount of anxiety among the Indian ruling classes.
To complicate matters more, Christian missionaries were greatly disrupting Indian society. They were challenging Hindu and Muslim practices all over India. They worked to emancipate women and to disrupt the ancient caste system. All of this was viewed with great suspicion by many Indians.
These forces of westernization greatly worried many Indians. The spark that ignited the powder-keg was the rumor of pig and cow fat in the rifle cartridges used by the Sepoys described in the other educator's answer. While there may not be any validity to these rumors, the fact that the mere idea of it instigated a rebellion shows that there was extreme animosity and distrust between the Indians and the British over their cultural differences.