Light has a dual nature: it sometimes seems particle-like and sometimes wave-like. It turns out that this is also true of electrons and all other particles...
It shows the inability of the classical concepts "particle" or "wave" to fully describe the behavior of quantum-scale objects.
"It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do". ("Complementarity and the Copenhagen Interpretation of Quantum Mechanics", By Harrison, David (2002), Dept. of Physics, U. of Toronto.)