A paid day's work in which the employee is allowed to stay at home for rest and relaxation.
This is a UK phrase that originated from workplace practice began in the 1960s there and in the USA. The first recorded reference to it is in September 1996 when The Financial Times reported:
... To staff at Text 100Italic, a PR company, there is a third option. They can take a "duvet day". Each employee is allowed two days a year when they can play hookey with their employer's blessing.
The figurative use of the term has also begun to be used. The Usenet newsgroup uk.local.london in March 2001 included this comment:
"The news server at Demon has decided to have a duvet day today."