I have to copy files along with the database?
Yes.
Isn’t the whole website contained within the database?
No.
Then what’s the point of backing up the database, if it won’t backup the files with it?
The physical files located in your web space make up the platform upon which the information located in your database is displayed. Your files also provide the foundation for the physical appearance of your web site. WordPress core files, theme files, plugins and extensions all reside in your physical files. Your content, is stored in your database. Two separate entities, that function together to make your web site work. This is true with any web based platform that takes advantage of SQL, not just WordPress. Learning how to take care of these is also a basic prerequisite for owning and maintaining a web site. You can find some detailed information and instructions on how to backup your WordPress files and database located here in the WordPress documentation: WordPress Backups That page also includes Database Backup Instructions