I am the developer of Akeeba Backup. There are two different CRON scripts supplied with Akeeba Backup Professional.
The recommended method is using the native CRON script which bypasses the web server entirely and runs the backup process essentially as a standalone PHP command line application. But that's not the object of your question.
The legacy backup method uses a special front-end URL indeed. The first URL you hit starts a backup using a specific profile and records that in the database under a specific Backup ID. Some backup work runs. At this time the backup engine state is serialized and committed to temporary storage. An HTTP redirection is issued. When you hit the new URL the backup engine state is read from the temporary storage, unserialized and the backup process resumes. This serialization/redirection/unserialization dance continues until the backup is complete.
Second and most important is understanding why that works, at all. Because of the serialization/unserialization the internal backup engine state is preserved through the redirection. The trick is that the backup engine uses a Factory object with support for serialization and unserialization. I have blogged about it in October 2009 at my site, dionysopoulos.me. Search Google for "A serializable PHP5 Factory pattern" on my site.
That serializable factory is exactly how the backup engine knows where the backup is up to every single time you resume the backup on a new page load. You are welcome to use this code on your projects implementing a long running process.