Short answers, pulled from the story.
An asteroid family is a population of asteroids sharing similar proper orbital elements, including semi-major axis, eccentricity, and orbital inclination. Members are thought to be fragments produced by past collisions between larger asteroids, either from complete shattering of a parent body or from a large cratering event that ejected material without destroying the parent.
Japanese astronomer Kiyotsugu Hirayama (1874-1943) first identified several prominent asteroid families in 1918. He recognized the Koronis, Eos, and Themis families initially, then later added Flora and Maria. In his honor, asteroid families are sometimes called Hirayama families.
About 33% to 35% of asteroids in the main belt are family members. A 2015 study identified 122 notable families containing approximately 100,000 member asteroids from a catalog of nearly 400,000 numbered minor planets.
Asteroid families are thought to have lifetimes on the order of a billion years, significantly shorter than the age of the Solar System. Age estimates for individual families range from hundreds of millions of years down to less than several million years, as in the case of the compact Karin family.
A nominal asteroid family is a rigorously identified grouping with distinct boundaries in orbital element space. A clan, such as the Flora family, merges gradually into the background population and may consist of overlapping unrelated groups. A clump has relatively few members but is clearly distinct from the background, while tribes are groupings too statistically uncertain to be confidently classified.
The Yarkovsky effect is a subtle force from sunlight that nudges small asteroids toward orbital resonances with Jupiter over time. Once small family members reach these resonances, they are relatively rapidly ejected from the asteroid belt, contributing to the gradual decay of asteroid families over millions to billions of years.