Short answers, pulled from the story.
The Curtain Theatre was an Elizabethan playhouse that opened in 1577 in Hewett Street, Shoreditch, just outside the City of London. It was London's second playhouse, built about 200 yards south of The Theatre, which had opened in 1576. It staged plays until at least 1624, with no records surviving after 1627.
The name came from Curtain Close, the plot of land on which the theatre stood. That plot took its name from the curtain wall of the nearby Holywell Priory, a curtain wall being a section of defensive masonry running between two bastions. The name has no connection to the stage curtains associated with modern theatres.
Shakespeare appeared as an actor in Ben Jonson's Every Man in His Humour at the Curtain in 1598. His company, the Lord Chamberlain's Men, used the Curtain as their main venue from 1597 to 1599. Plays performed there during that period included Romeo and Juliet and Henry IV Part I and Part II.
Excavations confirmed in May 2016 that the Curtain was rectangular, measuring roughly 22 by 25 metres. This surprised scholars, who had expected it to be round or polygonal like many Elizabethan playhouses. Walls survived up to 1.5 metres high in some places.
The term originated from the practice of collecting theatre admission fees in ceramic boxes. At venues including the Curtain, these boxes were carried to a counting room to be smashed and the coins tallied. That counting room was called the box office, and the name passed into everyday use.
In 2012, archaeologists from MOLA (Museum of London Archaeology) announced the discovery of the Curtain's remains during trial excavations in Hewett Street. Excavations through 2016 revealed the theatre's rectangular shape, a stage tunnel accessed through doors at each end, ceramic money boxes, a late 16th-century bird whistle, and a small statue of Bacchus. The site was designated a Scheduled Monument in August 2019.