System Safety can be thought of as the product safety function of Systems Engineering. The goal of System Safety is to identify risks inherent in a design and suggest risk mitigation measures as the design progresses. This means that the system safety engineers need experience with the type of system being designed, the risks presented, and safeguards used in the past. See the primer developed by the New England chapter of the System Safety Society.
Risk is defined as part of the System Safety process, usually as part of the process or specification called for by the overall system specification. The definition of risk will include a method of combining the probability that an event will occur with the severity of the consequences if it does occur. Categories of both probability and severity are identified in the System Safety process or specification.
As the design progresses, hazards are identified and tracked. A hazard is a scenario which can lead to a loss. Hazards are tracked throughout the design process so that the risk and mitigation measures associated with each are available to decision makers. Hazards with risk above a specified level at the end of the design process will have to be accepted by the decision makers (or will not be allowed at all, depending on the process being followed).
Hazard Analyses are conducted throughout the design cycle to document the assessment of risk associated with each identified hazard. The analyses start with generic hazards and control measures associated with the type of project being developed and progress to more specific content as the design progresses.
Specific design standards such as industry standards for specific products are brought into the analysis process as the design reaches a point where they can be applied.
A design priority is a key part of System Safety engineering. The most desirable option to reducing the risk associated with a hazard is to eliminate the hazard. If a function can be done with a toxic chemical for instance, the elimination of the chemical will eliminate the need for controls, warnings and training which are lower-priority design options.
Wikipedia article on System Safety
Nancy Leveson on Concepts of System Safety