Web Server: Yes, it is helpful to install something like Apache or Nginx in front of Alfresco to be the termination point for SSL.
Application Server: Yes, Alfresco requires an application server, and if you use the 5.2 installer you'll get Apache Tomcat.
Database Server: Yes, Alfresco requires a database server because that's where the metadata and other operational data gets stored. If you use the 5.2 installer you'll get PostgreSQL. Many people use MariaDB instead. Enterprise customers can use proprietary databases like Oracle or MS SQL Server.
Document/File Storage Server: This is Alfresco unless you are talking about where the content is physically stored, in which case you may be talking about a NAS/SAN. For some installations, local volumes are fine. For larger installations people often map their content store to a NAS.
Backup Server: Not enough context here, but, in general, yes, you need to take backups and you need to be able to start up a new server if something goes wrong.
In very small installations your web server, application server, and database server can all be on one machine. In most cases the database server is a separate machine. The web server and app server usually only need to be separated if you are building a cluster, which is only supported in Enterprise.
