He noticed that the predicted transits of Jupiter by its satellites would come over an hour after they were scheduled, and concluded that this was because light took time to get from Jupiter to earth. SInce the distance to Jupiter was known, it was a simple matter to divide this by the delay time to get the velocity of light pretty accurately. Today, thanks to high speed electronics, you can measure time intervals to nanoseconds, during which time light travels about a foot or so. As for what light is of itself, the answer depends on whether you which to speak the language ot particles or waves. Both are equivalent and self consistent, but I prefer the particle description to guide my feeble intuition.
Light is composed of particles called photons.
Each photon is a discrete packet of electromagnetic energy which travels at, what else, the speed of light. The amount of energy that each photon carries is determined by its size, which in the wave description, is just the wavelength of the light wave. Each quantum can be thought of as one complete oscillation of the electromagnetic wave. Exactly what is light, we don't really know other than in the quantitative details of the above description. The above description IS what light is, just as the detailed description of a dog is what a dog is.