Here are a few blurbs about the festival, from their website:

Artists appearing at the festival in 1996 included:
Van Morrison
Carlos Nunez
Capercaillie
Martyn Bennett
June Tabor
Tony McManus
The Fureys
Carol Laula
Janis Ian
Pearlfishers
Steve Riley and the Mamou Playboys
Natalie MacMaster
Swap
Brian Kennedy
Nollaig Casey
Dick Gaughan
Kathyrn Tickell

"What a start to Celtic Connections 1996. Concert goers were treated to a Gala Concert featuring the legendary French jazz violinist, 89 year old Stephane Grapelli performing with Galway fiddler Frankie Gavin. The repertoire covered everything from Gershwin, Irving Berlin, Cole Porter and Django Rheinhardt.

24 year old Alison Krauss ended a busy festival. Her album "Now That I've Found You" swept the boards at the 1995 Country Music Awards. Even at this point in her career she was credited as the women who brought bluegrass back into the mainstream of country music's consciousness."

The word 'connections' should be the tip off. Not just a festival celebrating Celts only by Celts only (that would be absurd in this day and age), but people the Celts are connected to by geography, cultural and musical similarities, that sort of thing, in a roots & shoots sort of way.