Sigma level expresses how many standard deviations fit between a process's mean and its nearest specification limit — the more that fit, the fewer defects. A 3σ process yields about 66,800 DPMO; a 6σ process just 3.4 DPMO (allowing for a 1.5σ long-term shift).
It gives a single, comparable number for process quality across any process. Sigma level relates directly to Cpk and is the namesake goal of Six Sigma.