Someone who's glowering has a dark, angry expression on her face. A glowering principal marching abruptly into your classroom probably means someone's in trouble.
If you wear a glowering expression, people are going to assume that you're mad at them — or just having a terrible day. The adjective glowering began with the verb glower, "to scowl," which had the 14th century meaning "to shine," and later "to stare with wide eyes." This sense of staring shifted around the beginning of the 18th century to mean "stare angrily."