A royal charter is a legal document issued by the monarchy which gives certain rights to an organization.
When an organization, for example: a university, is founded there has to be an official document which lists the basic laws (the constitution) of the organization. If this document is given to the organization by the king or queen it is called a Royal charter.
In Europe Royal charters have been used to create towns ever since the Middle Ages. The date when the charter was made is thought of as the date when the town was founded (started), even if there had been people living there many years before.
Many groups such as the British East India Company were formed by Royal charter. Most British university operate under Royal Charters. This gives them the right to give degrees to the students at the end of their studies.
The BBC operates under a Royal Charter which lasts for a limited period of ten years, after which it is renewed.
Charities may also have Royal charters. They do not need to have one, but they are likely to be more successful if they have a Royal charter.