Spot price is the current market price of particular stock or index in the spot market, which is also called as cash market. If you want to buy particular stock, you would pay the spot price.

The future price is the price of the same stock at a future date. The price which you would pay today for the right to receive the stock at some point of time in future, say after 3 months.
The difference between the spot price and the futures price is due to cost of carry. Cost of carry is the cost attached with holding the physical stock for a specified period of time such as, insurance, interest, etc.

If futures price is higher than the spot price, this is known as Contango and, a situation in which the futures price is lower than the spot price is said to be in Backwardation. We often use terms like PREMIUM for contange and DISCOUNT for backwardation.