When combined, 性格 (xìnggé) becomes “personality” or “character”—the nature and pattern of a person. Adding 不合 (bù hé)—literally “not a fit”—creates the full phrase 性格不合, meaning “personalities that do not fit together.”
The importance of 性格不合 goes far beyond its literal translation; it's deeply rooted in Chinese cultural values.
This phrase is extremely common and used in several key contexts.