How to delete backups made using Clockworkmod?
Clockworkmod stores its backups in /sdcard/clockworkmod/backup (replace /sdcard with the path for your external card if you're looking for backups to external memory). With versions prior to 6.0, you can move off (or delete) the entire directory to clear space. The entire backup is self-contained.

If you're using a 6.0 or greater version of Clockworkmod, this is no longer the case. The information about the backup is still in /sdcard/clockworkmod/backup, but the actual data is now stored in /sdcard/clockworkmod/blobs and is deduplicated between backups. The upside is that this should save some space between multiple backups. The downside is you can't just move off or delete a backup directory. With 6.0+, you now have to delete that folder, and then run the "free space" option. Initiating a new backup will automatically free space.