In this case, the phrase means "They will not discover that I did this."

For example, if I stole your lunch but threw away the evidence, I might say:

"I took his lunch, but he'll never trace it back to me. Maybe he will blame my cowrker instead." ;)

A quote from a film: "they cannot trace this back to me"

"They cannot trace this back to me." Could you explain what does mean "this back to me" means?

To trace can mean to follow... so "they cannot trace this back to me" means they cannot start at the results of the persons action, then follow it back to the person who did it. I hope that's clear. :)