The STRIKE PRICE is the price of the STOCK that you are "insuring".
If I BUY a $19 STRIKE PRICE PUT option that expires on OCT 20th, then the sellers are agreeing to buy the INTC shares at the $19 strike price. Someone will sell me the right to make them buy my INTC shares at $19. That is not very valuable when Intel is trading at $21.80.
How much would I have to pay to have someone buy my shares at a $20 strike price, on or before Oct 20th. 6 cents
$21 strike = 20 cents
$22 strike = 60 cents IN THE MONEY
$23 strike = $1.34
$24 strike = $2.27
$30 strike = $8.25 Notice that there is near zero premium for deep in the money option strikes. $30 - $8.25 = $21.75
The $2.18 pricing implies that you are looking at the $20 JAN2013 Call options. The call is IN THE MONEY.
I think you are saying it correctly. If you buy one call option contract for $2.18 per share, you will pay $218 plus trade costs and you can then purchase 100 shares of Intel at $20 anytime up to the expiration day. You own the option you bought and can exercise it at your descretion ... any time before expiration.
Your reward will be you effectively own the shares by owning the call option and your risk is limited to the $2.18 if Intel goes lower than $20.
The CBOE and Option Clearing Corporation have some good online training courses. Look under EDUCATION or COURSES.