What does the term dual "nature of light" mean?

The dual nature of light means that, in some experiments, light behaves as a wave. In other experiments, light behaves as a particle.

In 1801, Thomas Young shined light between two adjacent slits. The light waves interfered with each other and formed an alternating pattern of light and dark bands; the light bands are the constructive interferences, and the dark bands are the destructive interferences. If the light consisted of small particles, the alternating light and dark bands would not have occurred.

This picture explains it:

In 1905, Albert Einstein's photoelectric effect experiment showed that a beam of light could eject electrons from a metal. He proposed that light consists of photons with an energy that depended on the frequency (##nu##) of the light and that a photon with a frequency over a certain level (##nu_o##) would have sufficient energy to eject an electron. The light was behaving as a stream of particles, like machine gun bullets.

This picture shows the trend:

(lower wavelength = higher frequency)