From Asimov’s Guide to Shakespeare, p. 50–51:
A Midsummer Night’s Dream
… the triple Hecate’s team
The play within a play ends with a dance and with its audience amused and ready for bed.
Nothing remains but the final bit of entertainment, supplied by the fairy band. Puck comes on the stage alone to say that with the coming of night once more the fairies are back:
… we fairies, that do run
By the triple Hecate’s team,
From the presence of the sun
Following darkness like a dream,
Now are frolic.
– Act V, scene i, lines 385–89
Hecate was supposed to be one of the Titanesses in Greek mythology, but in the struggle that resulted in their supplanting by Jupiter (Zeus) and the other later gods, Hecate sided with Jupiter and remained in power. She was probably another personification of the moon.
There were three common goddesses of the moon in the later myths: Phoebe, Diana (Artemis), and Hecate. All three might be combined as a "triple Hecate" and Hecate was therefore frequently portrayed with three faces and six arms.
Later mythologists also tried to rationalize the difference in names by saying that Phoebe was the moon goddess in the heavens, Diana on earth, and Hecate in the underworld.
This connection with the underworld tended to debase her and make her a goddess of enchantments and magic spells, so that the fairies in following "triple Hecate’s team" were following not only the pale team of horses that guided the moon’s chariot (hence were active at night rather than by day) but also shared her power of enchantment and magic.
Her enchantments and magic made her sink further in Christian times until Hecate finally became a kind of queen of witches, and she appears in this guise in Macbeth…