A dactyl is a poetic foot of the form >-- (ON-off-off). For example, interstate, realize, microphone, cereal, limerick, etc. etc. A double dactyl is two dactyls in a row.
A double dactyl is also a verse form, otherwise known as "Higgeldy piggeldy". Like a limerick, it has a rigid structure and is usually humorous. Two stanzas, each comprising three lines of dactylic dimeter followed by a line with a dactyl and a single accent. The two stanzas have to rhyme on their last line. The first line of the first stanza is repetitive nonsense. The second line of the first stanza is somebody's name -- strictly speaking, a proper noun. Note that this name must itself be double-dactylic. There is also a requirement for at least one line of the second stanza to be entirely one double dactyl word, for example "Va-le-dic-Tor-i-an".
A classic example by Theodore L. Drachman:
A wonderful one by Paul Pascal on the subject of Antony and Cleopatra:
A similar verse form called a McWhirtle was invented in 1989 by American poet Bruce Newling.