Short answers, pulled from the story.
The Nice model is a scenario for the dynamical evolution of the Solar System, proposing that the four giant planets migrated from an initial compact configuration into their present positions long after the protoplanetary disk dissipated. It was developed in 2005 at the Côte d'Azur Observatory in Nice, France, and first published as three papers in the journal Nature.
The Nice model takes its name from Nice, France, because it was initially developed at the Côte d'Azur Observatory, which is located there. The pronunciation of the model follows the French city name, rendered as "niːs".
Jupiter and Saturn reaching their 1:2 mean-motion resonance triggered the instability, meaning Saturn's orbital period became exactly twice Jupiter's. This amplified the orbital eccentricities of both planets, destabilizing the entire planetary system and causing Neptune and Uranus to be flung onto more eccentric orbits.
The Nice model was originally designed to explain the Late Heavy Bombardment, a hypothesized spike in impacts on the Moon and inner planets roughly 600 million years after the Solar System formed. However, newer studies of lunar craters show exponential decay in crater numbers rather than a peak, and isotope measurements on Vesta are in tension with the bombardment hypothesis, casting serious doubt on the model's explanation.
The five-planet Nice model, developed by David Nesvorný and others, proposes that the early Solar System had five giant planets rather than four, with one being ejected during the instability. A 2015 study found this version has a statistically small likelihood of reproducing the current orbits of the terrestrial planets.
In the Nice model, Neptune was scattered outward to a semi-major axis of roughly 28 astronomical units with an eccentricity as high as 0.4, disrupting the outer planetesimal disk and trapping objects in resonances that form the Kuiper belt populations. Objects scattered onto orbits of roughly 5,000 astronomical units had their perihelia lifted by the galactic tide, forming the inner Oort cloud, while those reaching even larger orbits were perturbed by nearby stars to form the outer Oort cloud.