What is the external disk?
Is it new? If so, maybe it has a Windows file system on it (FAT, exFAT, or NTFS). If so then reformat to "HFS+ Journaled".
What backup utility are you using? TimeMachine, Carbon Copy Cloner, SuperDuper, etc...? If the external is suppose to be bootable because you are using a cloning backup (CCC or SuperDuper), then it is also important that the disk partition table be GUID.
You can find out this information via Applications -> Utilities -> Disk Utility, select the disk (not volume on the disk) and the partition time will be shown at the botton of the window. Now Select the volume and it will tell you how the file system on the disk is formatted.
Also do you want to leave room for a recovery partition on the external disk? Then repartition it with a small (2GB) partition that can hold a bootable recovery partition that you can setup via the Apple "Recovery Disk Assistant" which can be downloaded from Apple.