Short answers, pulled from the story.
Recusancy was the refusal of Catholics to attend Church of England services after the English Reformation. It was made illegal by the 1558 Recusancy Acts under Elizabeth I, which imposed fines, property confiscation, and imprisonment on those who stayed away from Anglican worship.
The Recusancy Acts remained on the statute books from 1558 until 1888, a span of three hundred and thirty years. They were temporarily suspended during the Interregnum of 1649-1660, mainly to relieve Nonconformist Protestants rather than Catholics.
The Howard family, now known as the Fitzalan-Howards and Dukes of Norfolk, are considered the most prominent Catholic recusant family in England. Other significant recusant families included the Welds, Arundells, Blundells, Petres, Throckmortons, and the Acton family, also known as Dalberg-Acton.
Shakespeare himself was a conforming member of the Church of England, but his mother Mary Arden came from a conspicuously Catholic family in Warwickshire. A tract professing secret Catholicism, reportedly signed by his father John Shakespeare, was found in the eighteenth century in the rafters of the family home, though the scholar Edmond Malone later declared it a forgery and the document has since been lost.
The Douay-Rheims Bible was an English translation of the Latin Vulgate made by expatriate recusants. The New Testament was translated in Rheims, France, in 1582, and the Old Testament in Douai, France, in 1609. Bishop Richard Challoner revised it across the years 1749-1752.
Guy Fawkes, Sir Robert Catesby, Christopher Wright, John Wright, Thomas Percy, and other recusants or converts were arrested on the 5th of November 1605, charged with attempting to blow up the King and Parliament. The plot was uncovered and most of the conspirators were tried and executed.