An irritable person gets annoyed quickly or easily. The spark is small; the reaction comes fast. People often become irritable when they are tired, hungry, too hot, in pain, or under stress, so the word can describe a passing state as well as a habit of temper. It is ordinary English, fine in speech and in writing, and a little softer than calling someone bad-tempered all the time. Though actually, doctors also use irritable for a part of the body that reacts too easily, as in irritable bowel (腸躁症 in Taiwan): the same idea of being set off too fast, but about an organ, not a mood. The everyday meaning you will meet first is still about a person's temper.