Mom, You Asked and Here It Is: Trip the Light Fantastic

Taken directly from Wilkepedia:

To "trip the light fantastic" is to dance nimbly or lightly, or to move in a pattern to musical accompaniment.

History
This phrase evolved through an interesting series of usages and references. The phrase is typically attributed to Milton's poem L'Allegro, but a somewhat similar phrase appears in Shakespeare's The Tempest. The phrase in this modern usage comes from the lyrics of the song The Sidewalks of New York. The following chronological list outlines a few notable usages of this and similar sounding phrases.
The phrase 'tripping on his toe' appears in William Shakespeare's The Tempest, written in 1611:

Before you can say come, and goe,
And breathe twice; and cry, so, so:
Each one tripping on his Toe,
Will be here with mop, and mowe.
In this context, "mop, and mowe" means 'a grimace'.

In the poem L'Allegro by John Milton, published in 1645, a similar phrase appears, which seemingly refers to the dance-like gracefulness of the goddess Mirth:

Come, and trip it as ye go,
On the light fantastick toe.
And in thy right hand lead with thee,
The Mountain Nymph, sweet Liberty;

The term trip in this passage means to step lightly or nimbly. The adjectives light and fantastick (as Milton spelled it) refer to the movement of the feet (toe, or dance step).

William Makepeace Thackeray borrows this phrase in Men’s Wives (published in 1843), as an elegant and humorous reference to dancing:

Mrs. Crump sat in a little bar, profusely ornamented with pictures of the dancers of all ages, from Hillisberg, Rose, Parisot, who plied the light fantastic toe in 1805, down to the Sylphides of our day.