Vesting as I know it, is when you have options for lets say 1000 shares, from the date of the granting, the shares would 'vest' on a schedule, in this example it would vest 25% over 4 years from the time of grant.

At year 1, 250 shares would be available for the employee to purchase at the price set at the time of grant.

Year 2, another 250 would 'vest' and so on.... until year 4 when they would be considered fully vested, now the employee can exercise the options, it doesn't mean that he owns them, but has the option to buy them.

Once fully vested, they would expire after a time period if not exercised.

hope that helps