The phrase often implies someone is overly emotional, beyond what is considered reasonable. He's in such a state over the traffic jam—it's just a small delay.
Pro Tip 2/3
Avoid Overuse
Overusing 'in a state' can dilute its impact, use it when emotions are genuinely high. She only gets into a state over really important exams, not just any test.
Pro Tip 3/3
Colloquial Usage
Common in casual conversation, less appropriate in formal writing or speaking. I wouldn't say I was 'in a state' during a job interview, but to a friend, sure.