No, it means that is only the notional value of that underlying asset of that contract, generally. The contract specification itself is listed on the exchange's websites, and there are really no assumptions you can make about a particular contract. Where S&P futures have one set of specifications, such as what it actually represents, how many each contract holds, how to price profits and losses... a different contract, such as FTSE 100 stock futures have a completely different set of specifications.
Anyway in this one example the s&p 500 futures contract has an "initial margin" of $19,250, meaning that is how much it would cost you to establish that contract. Futures generally require delivery of 1,000 units of the underlying asset. So you would take the underlying asset's price and multiple it by 1,000. (what price you use is also mentioned in the contract specification), The S&P 500 index is $1588 you mentioned, so on Jun2013 you would have to delivery $1588 x 1000, or $1,588,000.
GREAT NEWS, you only have to put up 1.2% in principal to control a 1.5 million dollar asset!
Although, if even that amount is too great, you can look at the E-Mini S&P futures, which require about 1/10th the capital and delivery.
This answer required that a lot of different subjects be mentioned, so feel free to ask a new question about the more specific topics.