Enable ZIP Compression
When BackupBuddy creates a backup file this is always created as a ZIP archive format file. Whether or not the files that are included in the archive are compressed in size is an option and this setting enables you to choose whether or not files will be compressed when stored within the archive.
The choice of whether to use compression or not is based on a time/space trade-off: if files are compressed it takes longer to produce the archive but the archive will (in almost all cases) be smaller in size; where as if files are not compressed the archive takes less time to produce but will (in almost all cases) be larger.
The reason why a compressed archive takes longer to produce is of course because the mechanics of compressing files is processor intensive and slower than just copying file content from one place to another.
The reason why, just sometimes, an archive containing compressed files may be larger than one containing the same files in an uncompressed form is that some of the files on your site may already be in a compressed format - particularly media files - and trying to compress an already compressed file, aside from being very processor intensive, can result in a larger file.
The default for this setting is checked, meaning that compression is enabled - this is usually the best option for most sites as it gives a good balance between speed of producing the backup and the size of the backup file. Another reason why you might want compression enabled is if you have a large site which approaches the size limits of the standard ZIP archive file format - around 4GB. Provided that you have no time constraint in producing a backup file then enabling compression means that you will get your site into a zip archive which you might otherwise not do if the files were included without compression.
On the other hand, if you have time constraints on producing your backup then you might want to consider disabling compression so that the backup file may be produced faster but of course at the expense of being larger.
Another reason you might want to consider disabling compression is if you have a large number of media files on your site - which as explained, may already be in a compressed format. It is worth experimenting in this case, try a backup with compression enabled, see how long it takes and how large the backup file is. Then try a backup with compression disabled and again how long does it take and how large is it. By comparing the two and based on your requirements and any other constraints you can decide whether it is better to have compression enabled or disabled on that specific site.