[What:]   When you create a backup task you can choose to preserve the directory structure of your backup source.
This is done in the section "Files>Locations" of the task settings.

[How:]    When this option is checked, the files will be back-upped to a path of the following structure:
[Target Path][Source Path]
instead of simply [Target Path].

Example:
Backup of files in source folder "C:\users\public\documents\" to target folder "N:\backup\documents\"
Will lead to saving the files in "C:\users\public\documents\" to "N:\backup\documents\C\users\public\documents\".

If you uncheck the "Preserve directory structure" option then the same backup action
will lead to saving the files in "C:\users\public\documents\" to "N:\backup\documents\".

[Why:]   The reason for this option is the following:
If you have multiple tasks that have the same target location, you might end up overwriting files with logically different files.

Example:

If you have two tasks:
1) source folder "C:\users\public\documents\" to target folder "N:\backup\documents\"
2) source folder "C:\users\some_user\documents\" to target folder "N:\backup\documents\"

If both source folders have the same file "some_file.docx" then these two logically different files will be back-upped to the same target file.
This is of course a problem.

Using more specific target folders is one option, though this might - in more extreme conditions - still lead to problems.

If you have two tasks:
1) source folder "C:\users\public\documents\" to target folder "N:\backup\documents\"
2) source folder "C:\users\some_user\documents\" to target folder "N:\backup\documents\some_user"

If source folder "C:\users\public\documents\" then has a sub folder "some_user", then you end up with the same issue.

The example above might seem trivial and easy to overcome by choosing good target folders, though in some cases you cannot be sure of which subfolders will be created over time , which possibly will lead to the described issue.
In these cases you should use the option "Preserve directory structure".

Untill version 1.9.6 this option was default enabled for new tasks.
As of version 1.9.7 this option is put to default disabled for new tasks.