‘Unity in diversity’ means that things which look completely different are, underneath, forms of one and the same thing. Applied to India, it means the country's many languages, dresses, foods, festivals and customs are not separate worlds that happen to lie side by side — they grow from shared ground.
The phrase reaches the chapter through Vincent Smith, who was troubled by the opposite thought. He asked how a single history could be written for so “bewildering” a country, and answered his own question: “the answer to the query is found in the fact that India offers unity in diversity.”
Unity = what you find when you look for what they share
Unity in diversity = both are true at once, and the second explains the first