Features
In Newton's corpuscular theory, a ray of light was a long stream of tiny particles or "corpuscles" that obeyed the same laws of physics as larger particles. These particles were extremely small and very light. Since they would nonetheless be subject to gravity, they would travel in a parabola just like a ball shot from a cannon; their speed was so great, however, that the influence of gravity on them appeared to be negligible.
Observations
Newton's theory was attractive precisely because it seemed to explain many of the phenomena he and other scientists had observed. Refraction, for example, could be explained as the net force on a particle of light traveling out of one medium into another. The different masses of the different colors of light would explain why each was refracted to a different degree. Reflection of light would just be a particle of light bouncing off a surface in this theory -- a simple and fairly intuitive way to understand what was happening.
Controversies
Newton's corpuscular theory, however, became more controversial than much of his other work. Fellow scientists Robert Hooke and Christian Huygens proposed that light actually consisted of waves, not particles, and this idea also seemed to fit well with many current observations. Nonetheless, Newton's reputation ensured that despite considerable controversy, his corpuscular theory remained dominant up until the 19th century, when scientists made discoveries that could not be reconciled with the corpuscular theory.
Diffraction &Interference
The decisive challenge to the corpuscular theory came from an experiment in 1801. The double-slit experiment showed that light shone through double slits created an interference pattern much like the one you would see with water waves crossing two "slits" in a sandbar. Despite this compelling evidence, some scientists still clung to the corpuscular theory until 1850, when another experiment demonstrated light traveled more slowly in water than in air -- and thereby refuted one of the predictions of the corpuscular theory. By the late 19th century, scientists saw light as an electromagnetic wave that could be described in terms of Maxwell's equations. In the early 20th century, however, this theory, too, was overturned by experiments that demonstrated light behaved both as a wave and as a particle -- and that other subatomic particles, like electrons, did so as well.