Price is determined by Supply & Demand, If the demand > supply, price goes up and vice versa.
The opening price is the price of the first trade that happens in that specific contract. Likewise for closing price too. The LTP of the last trade of the day for the future/option contract is considered the closing price.
If you are talking about ‘Settlement price’, then its computed considering the weighted average of the last 30 minutes of Nifty.