No, it's the pre decided amount that you have to pay to get every unit of share.
Taking an example of a publicly traded company, but the logic should stay the same.
As an example, if you have a contract with the strike price as 10 rupees, and the share is valued at 100.
That means that you pay 10 rupees per share to the company to "exercise" your option. And then you will be taxed on 100-10 according to the income tax rules.
If you have a contract saying that you will vest say 300 shares on a certain date, that means from that date till you exercise those shares, you will have to pay 10300 to the company, and the taxes to get shares worth 300100 in your demat account.
Now if the strike price is higher than the stick's valuation, that option is essentially worthless at that point in time, as you will be paying more than the share's value to get that stock.
I had a strike price of 1 rupee per share, and that seems fine to me. Don't chase an absolute zero strike price I think.