What the option means is that, assuming you meet all of the qualifications in the accompanying documents, you will be able to purchase 100 shares of the company at a price of $11.71 per share. You will then be able to sell those shares at the market price after you receive them (assuming you meet all of the securities law requirements, which should be minimal or non-existent to you if this is a large, public company).
Somewhere in the documents there should be a section about how and when you can exercise the options. Typically, you will not be able to exercise the options for at least a year, and you may not be able to exercise them after you have left the company. Also, because it says “vesting start date”, I suspect that the options will “vest” over a period of time, meaning you will only get part of the options unless you stay with the company for a specified time period.
(The documents should also specify whether they are qualified incentive stock options or non-qualified, which as noted above may have tax consequences).
Normally, to exercise the option, you will have to fill out a form (which is often attached to the option paperwork) and pay the company the exercise price for the number of shares of the option you want to exercise. If you wanted to (and were permitted to under the documents) exercise for all 100 shares, you would send in a check for $1,171.00 and the company would send you a certificate for 100 shares. You could then take that share certificate to a broker, who could sell it for you on the market (or you could hold that certificate and collect dividends if the company pays any). The company may also have a program where it will sell the stock for you at market price without having to separately go to a broker.
The documents may also have a provision for a cashless exercise, under which instead of paying the company $11.71 per share and getting the shares, which you then can sell in the market, the company will just pay you the difference between the $11.71 per share and the market price. In other words, if the stock is trading at $20.00, you would have a gain of $8.29 per share. Instead of giving them a check for $1,171.00 and getting back $2,000.00 after the sale, they will just give you the net difference of $8.29 per share.
Unfortunately, you may just have to read through the documents as best as you can. Usually there will be someone in human resources who can explain it to you and answer your questions. Good luck.