The basics of emptying trash?

After decades using Mac computers, I thought I knew how to empty the trash, but here's anew scenario:

I have an external hard disk mounted; I am using Aperture; I use Time Machine to backup onto the external.

I wanted to delete lots of very old backups, so I did the 'normal' thing: put them in the trash on Finder. After considerable time on the rolling progress bar, I get a message that says 'the vault is in use . . . ' and certain files cannot be deleted. I click continue. Over 20,000 files are deleted, and as the number decreases under the progress bar toward zero, it then goes NEGATIVE. Whatever that means. After more minutes . . . . the trash is 'empty,' except that it's not. A folder still remains. This untrashable folder contains something nested in other folders call 'boot.efi.'

Computer runs fine, but I'd like to learn what's happening, and what that stubborn file in Trash is about. Thanks to anyone who has time and patience to help me figure this out.