This is a very broad question and has many intricate answers. You might want to look at reports by Tanham which was published in 1992. It discusses India's strategic importance and its perception of itself with relation to its neighbors. This in turn has influenced its foreign policy. You might also want to check out the role of India in SAARC and BRICS as well as India acting as a "big brother". Alternatively, you can look at China's relation with Pakistan in terms of CPEC and OROB as well as its relation with Sri Lanka in building the Hambantota port
Very interresting and broad issue indeed! Of course they are all the questions related to the power of the nation considered. As much the power is, as much its capacity to act on the international stage with a strategic impact increases, making that State a strategic actor. But power is not everything. Some coutries which are not great powers or even regional power can have a strategic importance due to their ressources (Qatar, Bahreïn) or due to their geographical position such as Singapur. Also,to some extent, a small "country" such as the Vatican is strategicley important due to its influence (or soft power) to the Catholics around the world. I recommand you to read the book of zbigniew brzezinski "The grand chessboard".
Foreign policy refers to the strategic importance of a country, it can be depend on conutire's location, natural resources, population and political parties.
A number of factors amounts to a country's strategic importance in the international system. For example, a country's geopolitics( strategic location), military and or economic might, population, endowment with strategic natural resources and family of nations( belonging to a group of which you have history with, say Commonwealth countries), these are factors that influences a countries foreign policy. A country is strategically important if she has to some extent capitalized on any of these to influence her relations with others in the international system.@salampedia