It means at full speed. The trouble with it is that it's traditionally used by huntsmen, especially those hunting foxes on horseback.
Illustration by Henry Thomas Alken
This activity is now (rather controversially) illegal in Britain. People can still pretend to hunt, but they aren't allowed to pester any animals: instead they set the hounds to follow a synthetic scent, which provides a more reliable, and much safer, source of entertainment.
People still mourn the old ways, though, so perhaps the anticipation and danger were important.
(The foxes are now shot.)
Anyway, as far as I know tantivy may still be shouted when galloping after a scent-trail, but yelling it in any other setting is likely to get you scragged by any vegans or animal activists that might be lurking about the place.
They can be quite an aggressive bunch, the animal activists.
But still, if you feel a great need to shout tantivy at least you'll know they won't eat you.
Word Not To Use Today: tantivy. This word is probably an imitation of the rhythm of a galloping horse.