Preemptive rights give an existing shareholder of a corporation the right to purchase a proportionate part of any new share issuance before the shares are offered to non-shareholders. The purpose is to prevent the dilution of your ownership percentage and the right of control when new shares are issued.
For example, if you own 1000 of 2000 issued company shares, then you own 50% of the issued shares. If the directors decide to issue another 1000 shares to someone else, you will own 1000 of 3000 issued shares or 33% of the total issued shares. Basically, your ownership percentage has been reduced or diluted from 50% to 33.33%.
If you were entitled to preemptive rights, you would have the option (but not the requirement) to purchase enough additional shares to try to maintain your 50% ownership. Under most state incorporation laws, preemptive rights are not automatic. To have them, they must be agreed to by the incorporators and included in the incorporation articles.