Originally, light was believed to be consisted of continuous electro-magnetic waves of different wavelengths for each light color. But Albert Einstein then noticed that light that was emitted from something hot, like the filament of a light bulb for example, has the same energy distributions as a gas, with a peak intensity (=amplitude) in a specific energy level. This opposed to the idea that scientists had for light, If light was a continuous wave, then its intensity should always increase with energy without a specific peak level.
Einstein first proposed that -similarly to a gas- light must also be composed by individual particles - the photons- since it behaves as a gas. A photon is the quanta of light - the basic particle that light is composed of. In other words, what Einstein proposed (and got the Nobel prize for this) was that, light is not a continuous wave, but rather a wave composed by tiny little particles (quanta) called the photons.
(n) a discrete amount of something that is analogous to the quantities in quantum theory
(n) (physics) the smallest discrete quantity of some physical property that a system can possess (according to quantum theory)
This proposition also explained some strange behaviors that physicists of that time had noticed when experimenting with light, like for example that light could knock-off electrons from specific metals and gas molecules.
Later on, Max Planck was asked to make a research for the account of the German Biro of Standards to make light bulbs more efficient. During his experiments he also noticed that the mathematical models for the waves were inconsistent to the results of his experiments. Here is a nice video from Minute Physics...