A rights issue is the term for when a company offers more of its shares to current shareholders, usually to raise extra capital. It differs from other additional shares offerings, where shares are available for any investor willing to buy.
The shares in a rights issue are not taken from the current outstanding shares of the company, but are instead taken directly from the company itself. By offering the new shares to existing shareholders exclusively, the company will hope to avoid diluting its stock too much.
Typically, a rights issue will offer shares at a price lower than the current market price, with a stipulation that the rights must be taken up within a time period. As an extra incentive, sometimes the shareholders will be able to sell the additional shares on to the general market.