Short answers, pulled from the story.
The University Wits were a group of late 16th-century English playwrights and pamphleteers educated at Oxford or Cambridge. Prominent members included Christopher Marlowe, Robert Greene, and Thomas Nashe from Cambridge, and John Lyly, Thomas Lodge, and George Peele from Oxford. Thomas Kyd is sometimes included, though his connection to either university is not confirmed.
The term was coined by George Saintsbury, a 19th-century journalist and author. It was not used during the lifetimes of the writers it describes. The term was adopted widely by 20th-century literary scholars and critics.
The University Wits prepared the stage Shakespeare inherited by establishing blank verse for dramatic purposes and creating the first powerful dramas in English. Shakespeare was born just two months after Marlowe. George Saintsbury argued that the actor-playwrights, with Shakespeare at their head, borrowed the improvements of the Wits and added their own stage knowledge.
They turned to theatre because the universities were producing more scholars than there were opportunities for educated men, a problem Francis Bacon discussed in his essay "Of Seditions and Troubles". Theatre was not their first choice but was one of the few available paths. The three Parnassus plays, written by Cambridge students, expressed the anxiety this situation created.
The "upstart crow" attack on Shakespeare appeared in the pamphlet Greene's Groats-Worth of Wit, published as the work of the recently deceased Robert Greene. Many scholars believe the pamphlet was actually written by Henry Chettle, who was himself listed by Saintsbury as one of the "irregular band of outsiders". The pamphlet addressed writers generally assumed to be Peele, Marlowe, and Nashe.
Greene and Nashe were better known for their controversial, risque, and argumentative pamphlets than for their plays, creating an early form of journalism in English. Greene has been called the "first notorious professional writer". Marlowe was the most famous dramatist among the University Wits.