As hinted at by the word "dual" within it, duality refers to having two parts, often with opposite meanings, like the duality of good and evil.
If there are two sides to a coin, metaphorically speaking, there's a duality. Peace and war, love and hate, up and down, and black and white are dualities. Another term for a duality is a dichotomy. Duality has technical meanings in geometry and physics. In geometry, duality refers to how points and planes have interchangeable roles in projective geometry. In physics, duality is the property of matter and electromagnetic radiation to be understood best through wave theory or particle theory.