A bank holiday was a day of leisure, usually held on a Monday, observed at least in the United Kingdom.
According to a story she once told Merry Gejelh, Clara Oswald once had a life-changing moment on a bank holiday spent in Blackpool. There, on a crowded beach, she got separated from her mother. Clara was afraid, but her mother's reassurances after the event allowed her to conquer the fear of getting lost. (TV: The Rings of Akhaten)
Jackie Tyler regularly used her bank holiday Mondays to watch Cliff Richard movies. This inadvertently helped her daughter, Rose, fit in better when she visited 1950s Britain, because the movies familiarised her with some of the lingo of that era. (TV: The Idiot's Lantern)
While looking for the Tenth Doctor, Minnie Hooper told Wilfred Mott and the rest of the Silver Cloak that she'd been locked inside a police box during the August bank holiday of 1962 and that she'd "misbehaved". (TV: The End of Time)