Can someone please explain how traders and investors use this price difference to trade?
People use the price difference for small arbitrage between the futures and spot markets, where the larger spreads are reflected in the options markets. The spread in the options market dictates the VIX which many investors also use in their decision making process.
And most importantly how the futures market affects subsequent moves in the stock market?
The futures market effects the stock market where large contract holders move the entire futures price. This causes reactionary moves amongst all of the aforementioned arbitragers, who are hedged between the futures and spot markets.
With the /ES this is reflected down to actual individual stocks based on their weightings in the S&P 500 index. Many of those stocks have smaller companies that are also linked to them, such as a widget manufacturer for a gigantic ACME corporation listed in the S&P 500.