The expression “to trip the light fantastic” means: To dance.
In full, the expression is “to trip the light fantastic toe.”
It comes from John Milton’s “L’Allegro” (1632), from the early lines beginning:
Haste thee Nymph and bring with thee Jest and youthful Jollity,
and going on to:
Sport that wrinkled Care derides,
And Laughter holding both his sides.
Come, and trip it as ye go On the light fantastick toe.