What is the Server ?
All advanced database management systems include some kind of service applications as part of the database system. For example, to use the SQL Server database, you must have an application called "SQL Server Engine" running on the computer. This application is a windows service (a hidden application that will start automatically when your computer starts and keep running always).
Your program (software) which need to access the database will not access the database file directly. Instead, your program will communicate with the database service application. It is the responsibility of this service to communicate with the database file and execute your commands.
When you install SQL Server on your computer, the SQL Server service will be automatically installed on your computer. When you write code to access database, you just write the ADO.NET code using C#, VB.NET etc. The .NET Framework will execute your ADO.NET code to communicate with the database server and database server will communicate with the database file to execute. All these happens without your knowledge. All you do is, write ADO.NET code to execute queries and you will get the results back.
To make your ADO.NET code work, the database service must be running. If somebody stop the service, your code will fail.
In case of file based database systems like MS Access or FoxPro, there is no database service involved. Your code will directly communicate with the database file.