"To trip the light fantastic" is a figure of speech meaning "to dance." It originates from a verse in John Milton's poem, "L'Allegro" (1632):

Haste thee Nymph and bring with thee
Jest and youthful Jollity (...)
Sport that wrinkled Care derides,
And Laughter holding both his sides.
Come, and trip it as ye go
On the light fantastick toe.

Milton uses "trip" in the sense of "to tread lightly, to skip, to move nimbly and lightly." Some dictionaries still carry this meaning. Over the years this has been distorted to "tripping the light fantastic", which to me comes off as a vague drug reference (my original impression was that it perhaps referred to tripping on acid or the like, which is frequently done when dancing at a club, and evolved into a general-usage term for dancing).

The phrase didn't become popular until the late 19th century. A classic usage is:

"The muse does not only stalk with majestic tread, but on occasion trips on a light fantastic toe."  -Somerset Maugham, "Cakes and Ale" (1930)

So now you see, it does not refer to tripping the fantastic light (whatever that means), but rather tripping in an archaic sense on a toe that is both fantastic and light.

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