Time-and-a-half is when a worker (or workers) is paid 1.5 times their usual hourly rate. It is usually paid as an incentive to work on a particular day (e.g. on Sundays) or as government-mandated compensation for having workers work on particular days (e.g. public holidays).
In the United States, this provision, as well as the minimum wage, was first instituted by the Fair Labor Standards Act. The act was passed in 1938, during the Great Depression. Overtime pay was not intended primarially as a bonus to the worker but as a penalty or fine upon the employer. In order to increase employment opportunities, Congress encouraged employers to hire more workers for the same amount of time: better three workers at forty hours per week than two at sixty per week.
In New Zealand, if a worker works on a public holiday, the worker gets time-and-a-half for the hours they worked, and a day in lieu, i.e. he gets his holiday a day or two later. This legislation explains the 10-15% surcharge and/or special offers not being available on public holidays.