It's a great tune and Kevin Burke does a great version of it.

This is the information from Fiddler's Companion:

KING OF THE FAIRIES, THE (Rí na Sideog). AKA and see "King William of Orange" and "Bonnie Charlie [1]." Irish, Set or Long Dance. E Dorian (Mallinson, O'Neill): E Minor (Brody, Raven): G Minor (Welling). Standard. AAB (O'Neill): AABB (Mallinson): AABBCC (Brody, Raven, Welling). One tale attached to the tune has it that "The King of the Fairies" is a summoning tune, and if played three times in a row during a festivity the King must appear. Once summoned, however, the King assesses the situation, and if the gathering is to his liking he may join in; if however, he does not find it to his liking he may cause great mischief. "King of the Fairies" appears to be derived from a Jacobite tune called "Bonny Charlie," appearing in many 18th century Scots and Northern English publications, such as Aird (1783). Source for notated version: Dave Swarbrick (England) [Brody]. Brody (Fiddler's Fakebook), 1983; pg. 158. Mallinson (Enduring), 1995; No. 84, pg. 35. Raven (English Country Dance Tunes), 1984; pg. 168 (appears as "King William of Orange"). Welling (Welling's Hartford Tunebook), 1976; pg. 22. CAT-WMR004, Wendy MacIssac - "The 'Reel' Thing" (1994). Folkways FW 8876, Kevin Burke‑ "Sweeney's Dream." Transatlantic 341, Dave Swarbrick‑ "Swarbrick 2."

Cheers, S. in Seattle