The par value, or face value, of a share is the amount that is shown on the face of a share as its value.
The par value is an arbitrary amount that is determined when a company is incorporated. Its only real importance is that (in the UK at least) shares cannot be issued for a payment that is less than their par value.
It is possible to issue shares for a payment that is less than their par value, with shareholders then liable to pay the remainder later. This does not usual with listed companies' shares so it is of little importance to most investors.
The par value of a share multiplied by the number of shares is shown in a company's balance sheet as its share capital. When shares are issued at more than their par value the excess is added to the share premium reserve on the balance sheet.
A company can change the par value of its shares or adjust the amount in the share premium reserve, but it is not able to do so as and when the directors and shareholders wish. These changes require permission from a court and are usually associated with large returns of capital, share splits or consolidations.
What a company can freely do, is to use the share premium reserve for a scrip issue.
The par value must not be confused with the net assets (NAV) per share. The latter gives investors some information about what a share is worth, the par value does not.