• Eliminate waste, rework, and mistakes
• Increase customer satisfaction
• Increase profitability and competitiveness
• Statistical measure to objectively evaluate processes.

Six Sigma is used as a business strategy by concentration on Quality and defect reduction resulting in increase profitability and competitiveness. Fewer defects will lead to increased reliability and brand popularity.
Six Sigma is used as a metric to define the Quality of the output and ability of production process to produce defect free output.  
Six Sigma Is a Method for Continual Improvement. This is the most popular use of this word. A six sigma project has a defined method of an improvement project. These are DMAIC and DFSS.
Six Sigma is a Benchmark or a Goal to achieve the highest standard of productivity. A Six Sigma Quality is equal to less than 3.4 defects per million opportunities. This is the Vision for most of the organizations to make sure they deliver high quality to the customers.
Six Sigma is a Statistical Measurement to define the process Capability based on Standard deviation. For any normal distribution, the process capability is equal to six Standard Deviations.
Six Sigma is used in many other contexts which are most relevant and make sure customer satisfaction.
An organization can easily tell the customer about its quality by using the term six sigma.