What does it mean to backup a database What does it mean to backup a database?

My impression is that you would simply dump everything that makes up the database into some format that can be stored externally and used to restore from when needed.

Are there different levels of backups? For example, maybe it is not necessary to backup absolutely everything about the database. Data is critical, so the table structure is important, but there's probably more to databases than just that.
Database backups are copies of your database contents to prevent data loss in case of a disaster or data corruption.

There are two general types of backup Physical &amp; Logical. 

A Logical Backup 
exports the data stored in a table regardless of the location of the table.
Logical backups recreate the tables,indexes and insert all the data to the tables. Therefore, are relatively slower than physical backups. Depending on the RDBMS and the software you use you can change the way the logical backup is performed for the example you mentioned, in MySQL using mysqldump dbname --no-data  you can get a backup of table definitions without data in the tables for a database. A logical backup creates a file that when executed restores and recreates all the data in the database.

A Physical Backup 
is an actual copy of the data files that store a database's Structure,Index and Data which are on the hard disk.

One of the challenges of taking backups is making consistent backups.When a database is active it may change while the backup is being performed. 
During a hot backup( a backup when the database server is running) there are several methods to ensure consistency.

1) Using Table locks: Tables are temporarily locked and they won't execute any UPDATE, INSERT or DELETE.

2) Another method is using Multi-Version Concurrency Control (MVCC) where the database takes a point of time in the database as the backup reference point and backs everything up from there, while accepting UPDATE, INSERT or DELETE while backup is being performed. The advantage of MVCC is that the tables will completely operational while backup is taking place.

NOTE: Locking mechanisms depend on the RDBMS 

A Cold backup 
is another way to ensure consistency. In a cold backup the database server is turned off and not accepting any new clients.