Their are several kinds of security assessments. The security manager of a company can determine how well his policies and procedures are working, it depends on what the individual is looking for. On government contracts the agency awarding the contract will periodically send a team to review (assess) how well the company has implemented the requirements established by the contract. Essentially a security assessment is a review of the requirements for a particular contractor. In day to day work at the federal level, security reviews are conducted almost daily if classified information is involved.
Pretty straightforward: a security assessment is a measurement of the security posture (people, process, technology) of a system, facility or organization. The security posture is the way security is designed and implemented and typically identifies weaknesses and vulnerabilities in implemented security controls.