VeriSign Inc. is a company that specializes in domain name and CA stuff - in other words, it sells domain names and SSL certificates. Previously, they were mostly known for only the latter, but they bought Network Solutions Inc., the biggest domain registrar.
The company is a rather big player in name and certification business... and has been criticized for having bureaucratic inflexibility and having ocassional bad customer support (NSI was notorious for this) and doing interesting moves like recent proposed TLD namespace extension via browser plugins.