The territorial extent of the modern Republic of India is ultimately due to two factors:
The extent of the British Indian Empire, also informally called the "British Raj" or sometimes just "India."
The phenomenon of Muslim separatist nationalism, which became an increasingly potent force in the first half of the 20th century, and which eventually resulted in the Partition of India in 1947.
Or, to put it another way, the modern state of India inherited all territories of the British Raj that were majority non-Muslim, with the sole exception of the region of Kashmir (a Muslim majority region whose princely ruler elected to accede to India, and which remains disputed between India and Pakistan).
The non-Muslim regions of the Indian subcontinent which never became part of India, such as Nepal, Bhutan, Myanmar (Burma), and Sri Lanka, were not a part of the British Raj when India became independent. Nepal and Bhutan were separate entities under their own native governments who were part of the British sphere of influence, but were not subjects of the British Crown. In contrast, the Indian princely states like Hyderabad, Mysore, and Travancore were vassals of the Crown and were under the suzerainty of the Governor-General of India, and thus were considered part of the British Empire. Burma and Sri Lanka (Ceylon), on the other hand, were both part of the British Empire, but were separate colonies from India. Burma had previously been part of British India, but was separated from the Raj by the 1935 Government of India Act and was constituted as a separate political entity, and thus received independence separately from India/Pakistan (which both became independent in August 1947 by the provisions of the same legislative act, the Indian Independence Act). Ceylon had been a separate Crown Colony since the early 19th century, and thus also received independence separately from India, in February 1948.