Futures and options are contracts and similar to any other contract it is a contract between a buyer and a seller. Buyer is bullish (expecting the market to go up) and seller is bearish (expecting it to go down). Only when there is trade between a buyer and seller, a contract opens and all such open contracts are together called as open interest. So if I have bought 1 lot of Nifty expecting it to go up and you have sold 1 lot expecting it to go down, that makes it 1 open contract and hence the open interest of 1. Typically every derivative contract will have its own OI, Nifty August futures will have its own OI and September futures will have its own. Similarly, OI will be different for calls and puts of various strikes.
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