The vasty deep
I can call spirits from the vasty deep.
Why, so can I, or so can any man;
But will they come when you do call for them?
Why, I can teach you, cousin, to command
And I can teach thee, coz, to shame the devil—
By telling the truth. Tell truth and shame the devil.
The Welsh rebel Glendower parries with his "cousin" Henry Percy, a.k.a. "Hotspur," who is related to Glendower through marriage. These two have not been getting along, which has mostly to do with bad chemistry; each is addicted to a different kind of self-aggrandizement. As they plot against the sitting king, Henry IV, Hotspur mocks Glendower for his outrageous claims to control the devil and his spirits. While the hothead Hotspur easily tolerates his own brags, he has no use for Glendower's shady mumbo-jumbo and tales of his prodigious birth.
Glendower insists that he can call spirits from the "vasty deep," that is, from vast depths, presumably the underworld. "Vasty" appears to be a form Shakespeare invented and that has been picked up in homage. The suffix -y serves no real purpose, except perhaps to add a convenient syllable to fill out a blank-verse line. The suffix may also be intended to smack of pretense, and thus to expose Glendower's self-satisfaction with his own phraseology.