During the period of British rule in India, British monarchs were designated as the King/Queen of most of the nations in the British Empire, but for India, they were designated as Emperor or Empress. Why did they have such a special title for ruling over India?
I think you will find the answer to what you are looking for here and here. Those answers do a good job laying it out, so I won't add too much more.
In the 1870's (sometimes dated to a speech Disraeli gave at the Crystal Palace in 1872, praising Britain's Imperial aspirations and the maintenance of the empire), the idea of the empire was stronger and stronger in the UK. In 1876, Disraeli, who was then prime minister, offered the title of Empress of India to Queen Victoria, as commented on by this famous cartoon in Punch. So why take on the title? More than anything, because it lined up with shifting sentiment across classes in England towards the empire. There was a feeling across England embracing the empire and England's imperial role. Simply put, people were marvelously proud of living in the "empire on which the sun never sets." I've also read that the title of empress clearly placed Victoria over her princely subjects in the empire, since some of the princely titles in India could be considered equivalent to king/queen, such as the Maharaja of Travancore and the Nizam of Hyderabad.