In the context of Indian history, the principle of Dyarchy (diarchy) refers to

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The Government of India Act of 1919 was enacted to satisfy the people of India to some extent. The salient features of the Act were as follows:Preamble: The Act provided for a Preamble that laid down the basic principles and policies upon which it was based. According to it, the policy of the British Parliament was –to provide for the increasing association of Indians in every branch of Indian administration,to develop self-governing institutions with a view to the progressive realisation of responsible government in British India as an integral part of the empire;accordingly, the Preamble suggested for a decentralised unitary form of government.The Act divided the functions of government into two categories: central and provincial. The provincial subjects were further subdivided into transferred and reserved. Thus, in the provinces, a new form of government, dyarchy, was introduced. Dyarchy means dual set of governments, e.g. accountable and non-accountable. In the transferred subjects, the Governors were to be assisted by the ministers responsible to the legislature, while in the reserved subjects, the Governors were to be advised by the councillors who were not accountable to the legislature.Source: NCERT: Textbook Chapter 1 to 8 Indian Constitution and Administration Class 11