A share in a for-profit corporation that has some kind of special right or privilege attached to it, such as that it is distinguished from the corporation’s common shares.
The most common special right is a preference over holders of common shares when dividends are declared.
Another, is for the preferred shares to be redeemable at the option of either the holder or the corporation.
Still another might be to disallow voting rights to preferred shareholders.
Depending on the local laws in your state, there may be no limit to the qualifications a corporation can attach to preferred shares.
For example, a family corporation may only allow holders of preferred shares to use a recreational property belonging to the corporation.