Financial Terms - Underwriting

What does it means...
1. The process by which investment bankers raise investment capital from investors on behalf of corporations and governments that are issuing securities (both equity and debt).

2. The process of issuing insurance policies.

Investopedia says...
The word "underwriter" is said to have come from the practice of having each risk-taker write his or her name under the total amount of risk that he or she was willing to accept at a specified premium. In a way, this is still true today, as new issues are usually brought to market by an underwriting syndicate in which each firm takes the responsibility (and risk) of selling its specific allotment.

Details found here.

Rights which are underwritten would means that the underwriting company will take up the remaining unsubscribed rights.