Short answers, pulled from the story.
Ytterbium was discovered in 1878 by the Swiss chemist Jean Charles Galissard de Marignac. He identified a new component within the rare earth called erbia while examining samples of gadolinite, and named it ytterbia after Ytterby, the Swedish village near where the erbium source had been found.
Ytterbium is named after Ytterby because Marignac found its precursor, ytterbia, in minerals originating near that Swedish village. Ytterby is the source of four element names in total: yttrium, terbium, erbium, and ytterbium.
Ytterbium is mainly used as a dopant in stainless steel to improve mechanical properties, and as a doping element in solid-state and fiber lasers that radiate in the 1.03-1.12 micrometer band. The 169Yb isotope is used as a gamma-ray source in portable radiography and nuclear medicine, and the charged ion 171Yb+ is used as a qubit in trapped-ion quantum computers.
In 2013, a pair of ytterbium atomic clocks at the National Institute of Standards and Technology achieved stability to within less than two parts in one quintillion, roughly ten times better than previous records. At that level of accuracy, the clocks would not gain or lose a second over a period comparable to the age of the universe.
Ytterbium has a closed-shell electron configuration that gives it a significantly lower density, melting point, and boiling point than neighboring lanthanides. It also readily forms stable +2 compounds, a behavior rare in the lanthanide series, and is paramagnetic above 1.0 kelvin rather than becoming antiferromagnetic or ferromagnetic at low temperatures like most rare-earth metals.
Ytterbium is mined primarily in China, the United States, Brazil, India, Sri Lanka, and Australia, extracted from minerals including monazite, euxenite, and xenotime. Its average concentration in the Earth's crust is about 3 milligrams per kilogram, and global reserves are estimated at one million tonnes. World production is only about 50 tonnes per year.