A database management system is a suite of software applications that together make it possible for people or businesses to store, modify, and extract information from a database. Sound like something found only in bank vaults? It's not. You can find these systems in many places in your everyday life.
That ATM that you get cash out of every week is a database management system. When you make flight reservations online, you're providing information that is entered into such a system. Even the library that you or your children check out books from runs on one.
On a more personal level, your personal computer can have its own database management system. You might have spreadsheets that contain mountains of data. Any time you fill up a spreadsheet with data and run queries to find and analyze data in different ways, you are accessing such a system.
And how do you view the data that is the result of a query? By looking at a report. Most systems have a reporting function that is the last step in the data manipulation process. After all, collating the data without looking at it won't get you very far.
One of the main functions of the database management system is doing the heavy lifting for you. In other words, you don't necessarily have to know exactly where all that data is in the system; as long as the system knows where it all is, it can deliver a report for you to peruse. This might not seem to matter if you're thinking of just your computer, but throw in a mainframe that contains reams and reams of data, and we're talking about a huge amount of information that can be stored any number of places within the mainframe system. The result is the same, though: a report that you can read, analyze, and act on.
This functionality also extends to a multi-user database. Such a system under this scenario would allow you as one user to operate all functions within the database without having to know what other users are accessing the same database. One popular example of this kind of multi-user database is Microsoft SQL Server.