Why is my external HDD active when I'm not using it?

Solution 1:

It's probably the 'Spotlight' indexing that is busy indexing the drive 's content.

Solution 2:

This could be a few things:

• In case you chose to encrypt your backups, it may be FileVault2 is currently encrypting the disk. Here you find some instructions how to check that.
• As In the accepted answer, it could be spotlight indexing the disk.
• It could be your disk's firmware doing some maintenance task. However, in that case the indicator LED will probably not be flashing. I have a Seagate Archive HDD that uses shingled magnetic recording and practically after any write operation it does a few minutes of reorganising the data. This is done internally by the disk and is intransparent to the user and to macOS.