This is a conceptual aspect of the quantum theory. Bohr regarded it as an essential feature of the theory.
There are certain pairs of commentary properties that cannot both be observed or measured simultaneously. An example of this principle is the relationship between position and momentum.
Bohr supposedly conceived of this principle during a skiing vacation in Norway. (February and March of 1927) During this time he received a letter from Werner Heisenberg, regarding a thought experiment he had about a microscope using gamma rays. The thought experiment involved a trade off between uncertainties that would later be formulated as the Uncertainty principle.
Momentum would be meaningless and undefinable in a situation where position was calculated with precision.
Bohr would publicly introduce the principle of complementarity on September 16, 1927.
Indeed, according to the Heisenberg uncertainty principle, there is a limit to the precision that certain pairs of particle properties can be known at the same time. The example I gave above is position and momentum. A more general interpretation of this idea will be formulated by Bohr in 1928.
Niels Bohr formulated this "principle of complementarity" in 1928. These are complementary properties that cannot both be known precisely at the same time. Examples of complementary phenomenon are:
Position and momentum
Wave and particle
Energy and duration
Entanglement and coherence