A database is an organized place where a program stores information so it can find or update it later. It is like a filing cabinet whose contents can be searched quickly by computer.
An online shop might keep product names and order details in a database. When someone opens a product page, the website asks for the matching information and displays it.
The database is separate from the screen people see: it stores the information, while the website decides how to show it. Important data should also be backed up so it can be recovered after a problem.