It usually is translated as "frustrating" or "annoying" and from time to time, it can also be loosely translated as "suffocating".
1.영어로/한국어로 대화하기 힘들 때 기분이 답답해요? --> It's so frustrating (or annoying) when I find it hard to converse in English/Korean.
2. 집에 빨리 가고 싶은데 차가 막힐 때 기분도 답답해요? --> It's so annoying (frustrating) when I want to get home as quickly as possible but there's so much traffic.
3. 출근 시간에는 지하철에 사람이 너무 많아서 답답해요. --> So many people on the subway suffocate me (or "it's suffocating to be on the subway with so many people") during the morning rush hour.
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I've thought about the situations where I would use 답답해, 답답해요, 답답하다 and here is what I've been able to come up with:
1) The other person is (or people are) are so stupid and dumb, it actually frustrates you.
2) When you want to fix a certain situation but you find that there simply is no way... (That's frustrating..!)
3) Say I'm a prisoner but I'm in the prison because I was falsely accused of a crime I never committed. Super frustrating!!!
etc.
Hope that helps.