Six Sigma at many organizations simply means a measure of quality that strives for near perfection. Six Sigma is a disciplined, data-driven approach and methodology for eliminating defects (driving toward six standard deviations between the mean and the nearest specification limit) in any process – from manufacturing to transactional and from product to service. (Source)
A "Sigma" is the symbol for a standard deviation. Six standard deviations is equal to 99.9997% of whatever you happen to be measuring. In this case we measure "opportunities for a defect". A Six Sigma Process would have 3.4 defects per Million opportunities (DPMO).
You may think this only applies to an assembly line, but you would be incorrect. Each step in a process is a chance for error. Even in an office, our team can find and eliminate the opportunity for defects in your product or service.