When something happens or is done indelibly, it can't be erased or removed. If you label your sleeping bag indelibly with your name, you do it in permanent ink.
A memory might be indelibly etched in your mind — in other words, it's there for good. And when a serial number is indelibly engraved on your new computer, it can't be removed. Indelibly comes from the Latin indelebilis, a combination of in-, "not," and delebilis, "able to be destroyed," which is rooted in delere, "destroy or blot out."