Software Quality Assurance is a Set of Activities for Ensuring Quality in Software Engineering Processes (that ultimately result in quality in software products).

It includes the following activities:

Process definition and implementation
Auditing
Training

Processes could be:

Software Development Methodology
Project Management
Configuration Management
Requirements Development/Management
Estimation
Software Design
Testing

Once the processes have been defined and implemented, Quality Assurance has the following responsibilities:

Identify weaknesses in the processes
Correct those weaknesses to continually improve the process

The quality management system under which the software system is created is normally based on one or more of the following models/standards:
CMMI
Six Sigma
ISO 9000