A database is initially an organized collection of data. After digitization, for example, your customer data is in a sorted state in a database. This may not only be in one physical location, as you might think. Your data can also (especially if you work with a professional IT service provider) be kept in several places at the same time. The databases are then connected through a complex synchronization or backup process.
Data can also be saved in files, for example in Word or in simple text documents. The difference to a database lies in the searchability and speed. Individual data records in a database are always structured according to the same schema and their orderliness therefore does not depend on the level of knowledge or the format as observed by an employee entering the data.
The second benefit mentioned, searchability, is also a very important point. Data is stored in relation to one another in a database. This means that, for example, customers can be assigned to projects and then employees to the projects. This means that not only simple queries can be made using names or descriptions, but also complex statistics, affiliations or forecasts.
Finally, you should understand that you will probably never communicate directly with a database, based on text commands, but that you will use software as a graphical interface. For your own ideas and projects, your IT service provider first discusses the structures and relations with you and then develops the application interface.
This explanation applies primarily to relational databases. There are other variants, such as document-based systems, but these also have specific applications.