A stock option is the option to purchase shares in the company. Stock options are usually given to employees, not the founders. They are not shares, you are given the option to buy shares at a later date.
Strike price is the price on the paper saying how much you will pay for them, if and when you decide to exercise the these options. So the shares will hopefully have more value in the future compared to the strike price.
In the US startups, it's commonly 4 year vesting period with 1 year cliff. You have to work in the company for 1 year, them you get the first 25% of your options, and usually a small percentage monthly after that.
You can turn the bought shares to money on whey they do "an exit". When Initial Public Offering (IPO) happens or the company goes public, you can sell your shares for real money. There might be some holding period and other rules applied though.
Figure out how big percentage of the company does the shares present. You get this by asking the total number of shares currently.
As of 2016, engineers are in so high demand that options are just a bonus. You should never settle for smaller salary in exchange for options.