It is apparently a fantasy name, according to this exhaustive website about Scandinavian first names:
http://www.nordicnames.de/wiki/Tiril
So, I guess no one really knows for sure. At first glance, I would have thought that it is a combination of the name of the Germanic god
Tyr, and the Germanic element
hild "battle." But that will probably forever remain speculation.
"How do you pick up the threads of an old life? How do you go on... when in your heart you begin to understand... there is no going back? There are some things that time cannot mend... some hurts that go too deep... that have taken hold." ~
Frodo Baggins