Short answers, pulled from the story.
The Hilda asteroids are a group of more than 6,000 minor planets orbiting the Sun beyond the main asteroid belt but within Jupiter's orbit. They move in a 3:2 orbital resonance with Jupiter, completing three orbits for every two Jupiter completes. The group is named after the asteroid 153 Hilda.
The Hilda asteroids are named for 153 Hilda, the namesake object that gives the group its name.
More than 6,000 Hilda asteroids are known. A plot of the group made as of the 1st of January 2005 showed only a few hundred confirmed members, and research into their orbital patterns still relies on that smaller confirmed sample.
The Hildas Triangle is the triangular pattern the whole Hilda population traces when plotted at a single moment, with slightly convex sides and blunted corners near Jupiter's Lagrange points. The Hildas linger at the triangle's corners for 5.0-5.5 years on average and cross each side in 2.5-3.0 years.
The two known collisional families within the Hilda group are the Hilda family and the Schubart family. The Schubart family is named for the asteroid 1911 Schubart.
The Hilda asteroids appear brightest when Earth is in conjunction with the mid-sides of the Hildas Triangle, placing them in opposition to the Sun, an alignment that recurs roughly every four and a third months. At these times an object can appear up to 2.5 magnitudes brighter than a similarly sized Hilda near the triangle's corners.