Auditing, in the financial community, is done to verify the accuracy and integrity of financial records. Many standards have been established in the financial community about how to record and report a company's financial status correctly. In the computer security world, auditing serves a similar function. It is a process of assessing the security state of an organization compared against an established standard.
The important elements here are the standards. Organizations from different communities may have widely different standards, and any audit will need to consider the appropriate elements for the specific community. Audits differ from security or vulnerability assessments in that assessments measure the security posture of the organization but may do so without any mandated standards against which to compare them. In a security assessment, general security "best practices" can be used, but they may lack the regulatory teeth that standards often provide. Penetration tests can also be encountered- these tests are conducted against an organization to determine whether any holes in the organization's security can be found. The goal of the penetration test is to penetrate the security rather than measuring it against some standard. Penetration tests are often viewed as white-hat hacking in that the methods used often mirror those that attackers (often called black hats) might use.