To be unflappable is to be calm and relaxed, even in a stressful situation. A confident person is usually unflappable.
Some people get nervous and jittery under pressure, while others are unflappable. If you're unflappable, you stay calm, relaxed, and poised no matter what's happening. A good kindergarten teacher stays unflappable in the midst of chaos, and a successful businessperson is unflappable when faced with deadlines and unexpected problems. The earliest use of this word was in 1953, in reference to the British prime minister. At its root is flap, twentieth-century British slang meaning "disturbance or tumult."