The word leave or annual leave is synonymous with holiday in the sense of being away from work but it is used in a number of specific contexts.
For example, soldiers and army officers who want to visit their families or need a few days off for other reasons may apply for a leave (of absence). Leave also means time spent away from work for some specific reason, such as having a baby or being ill.
Mothers spending a year at home after giving birth to a baby are on maternity leave. But nowadays there are more and more fathers who opt for paternity leave, especially if the mothers have better-paid jobs.
If you get ill and are in full-time employment, you are entitled to paid sick leave.