The cost of carry explains the basic relationship of cash to futures pricing, but it does not explain many less certain factors that can affect futures pricing such as seasonal influences and other unpredictable events.
As for Interest-rate and currency futures - those based on T-bonds, T-bills, Eurodollars and the five major currencies - the biggest influences are the policies and trading activities of the Federal Reserve, U.S. Treasury and foreign central banks, all of which affect interest rates.
Stock indexes are affected by whatever influences the stock market as a whole. Interest rates certainly play a major role - higher interest rates usually hurt the stock market. Other effects include the overall prospects for corporate earnings and corporate tax policies that help or hurt big business.
Futures trading provides a way to establish a form of price knowledge leading to continuous price discovery. Futures prices reflect not only current cash prices, but also expectations of future prices and general economic factors.