Short answers, pulled from the story.
Sarnath is where Gautama Buddha delivered his first teaching, the Dhammacakkappavattana sutra, to five disciples around 528 BCE, making it the birthplace of the Buddhist sangha. The Buddha himself named it as one of four pilgrimage sites his followers should visit, alongside Lumbini, Bodh Gaya, and Kushinagar. It is listed as one of the eight most important Buddhist pilgrimage sites in the world.
Sarnath derives from the Sanskrit Saranganath, meaning "Lord of the Deer". The name refers to a Buddhist legend in which Siddhartha Bodhisattva, in a previous incarnation as a deer, offered his own life to save a doe, leading a king to declare the land a sanctuary.
Sarnath was attacked and plundered in 1194 CE when Qutb ud-Din Aibak, commander of Muhammad of Ghor's army, led forces from Ghazni to Varanasi and Sarnath. Some scholars, however, including archaeologist Giovanni Verardi, argue that Brahmin communities had already been expelling Buddhists and converting the site before the Muslim invasion arrived.
The Lion Capital of Ashoka is the carved summit of an Ashokan pillar erected at Sarnath, dating to approximately 241-233 BCE. It was uncovered during Friedrich Oertel's excavations in March 1905 and survived a 45-ft fall to the ground. It now serves as the State Emblem of India, and the 32-spoke wheel of dharma from the same pillar is incorporated in the flag of India.
Alexander Cunningham conducted the first systematic archaeological excavations at Sarnath in 1835-1836 at age 21, guided by the writings of the Chinese pilgrims Faxian and Xuanzang. By 1836 he had conclusively identified the site as the location of the Buddha's first sermon. Friedrich Oertel carried out the most extensive excavations in 1904-1905, uncovering the Ashokan pillar's lion capital and Schism Edict.
Sarnath has been nominated for UNESCO World Heritage status but had not yet been inscribed as of the nomination in 1998. The nomination covers two groups of monuments: group A is the Chaukhandi Stupa, while group B includes the remaining temples, stupas, monasteries, and the pillar of Ashoka.