Short answers, pulled from the story.
The speed of light in vacuum, denoted c, is exactly 299792458 metres per second. It is exact by international agreement, because the metre is defined as the distance light travels in vacuum in 1/299792458 of a second.
Accelerating an object with rest mass to the speed of light would require an infinite amount of energy, because its kinetic energy grows toward infinity as speed approaches c. Travelling faster than c would also violate causality, allowing an effect to be observed before its cause, which has never been recorded.
Ole Rømer made the first quantitative estimate of the speed of light in 1676 by studying Jupiter's innermost major moon, Io. He found that Io's periods appeared shorter when Earth approached Jupiter and deduced that light takes 22 minutes to cross the diameter of Earth's orbit.
Light travels slower than c in transparent materials, with the slowdown given by the refractive index. For visible light, glass has an index around 1.5, water around 1.3, and diamond around 2.4, while air is about 1.0003.
The speed of light became an exact defined constant in 1983, when the 17th General Conference on Weights and Measures redefined the metre as the distance light travels in vacuum in 1/299792458 of a second. Since then, better experiments improve the realization of the metre rather than the value of c.
The finite speed of light delays communication with spacecraft, growing longer with distance. Ground control waited at least three seconds for replies from Apollo 8 in lunar orbit, and signals to Mars take between five and twenty minutes depending on the planets' relative positions.
The origin of the letter c is unclear, with guesses including c for constant or the Latin celeritas, meaning swiftness. Max Abraham used c with its modern meaning in 1903, and Einstein switched from V to c in 1907, by which time c had become the standard symbol.