A bank holiday is a public holiday in the United Kingdom and the Republic of Ireland. There is no automatic right to time off on these days, although banks close and the majority of the working population is granted time off work or extra pay for working on these days, depending on their contract. The first official bank holidays were the four days named in the Bank Holidays Act 1871. Today the term is also commonly used for Good Friday and Christmas Day, which were already public holidays under common law and therefore not official bank holidays in England, Wales and Northern Ireland.
When the stated date falls on a Saturday or Sunday, the following Monday is normally designated a public holiday instead. For example, when Christmas Day falls on a Saturday - and, therefore 26 December falls on a Sunday - then Monday 27 December and Tuesday 28 December are the designated substitute public holidays.
The official list of public holidays can be found online: https://www.gov.uk/bank-holidays.
It should be noted that public holidays may be different in England & Wales vs Scotland or Northern Ireland.