My knowledge of Welsh is less than beginner, but there is a Welsh word siriol which means cheerful, and everything I come across seems to confirm that the name comes from that. The Welsh name book* I have lists it as
"The Welsh for "happy" or "content"". I'd also guess that the meaning "the bright one" would be somewhat correct, bright being a synonym of cheerful in the context.
If anyone who has a better knowledge of Welsh could confirm (or refute) this, then please do so.
* Welsh Names by D. Geraint Lewis, published by Geddes & Grosset.
"They thought the Library was a dangerous place because of all the magical books, which was true enough, but what made it really one of the most dangerous places there could ever be was the simple fact that it was a library."
http://www.babynames.com/namelist/9526469