In physics, especially in the quatum mechanics, the complementarity is a experimental result (also theoretically predicted) which states that objects have properties that are complementary to each other, but can not be observed or measured all at once. The Complementarity Principle, enunciated by Niels Bohr in 1928, are related to the so-called wave-particle duality: The wavelike and corpuscular behaviors are complementary properties of the same entity.
As Leonard unsuccessfully trying to explain to Penny on the day of their first meeting (S01E01: "Pilot"), before the formulation of this principle, scientists tried to find out whether light was a wave or a particle. Because the results of the double-slit experiment of Thomas Young, it was believed that light was a wave. However, with the emergence of the concept of photon we see that light is detected as wave or particle according to the experiment.