The huatou is a “living phrase” used in Chan meditation to push one beyond dualistic thinking. To get a better sense of how this is a “shortcut,” I’ll begin by citing Robert E. Buswell, Jr’s fine essay, “The ‘Short-cut’ Approach of K’an-hua Meditation.” In what follows, the first quote is from Buswell, Jr., the second from Chan master Ta-hui:

The purpose of the hua-t’ou, then, is to enable the student to transcend the dualistic processes of thought in a single moment of insight, without requiring that he “progress gradually through a series of steps or stages.” For this reason Ta-hui refers to k’an-hua Ch’an as a “shortcut” approach to meditation:

“If you want to understand the principle of the short-cut,
you must in one fell swoop break through this one
thought—then and only then will you comprehend birth
and death. Then and only then will it be called accessing
awakening….You need only lay down, all at once, the mind
full of deluded thoughts and inverted thinking, the mind of
logical discrimination, the mind that loves life and hates
death, the mind of knowledge and views, interpretation and
comprehension, and the mind that rejoices in stillness and
turns from disturbance.”

p. 81.

In a “single moment of insight”? In “one fell swoop?”–what does this mean?

Yes, the point is to be with the huatou–like “Who?” or “What?”–so intently and intensely until the wonderment becomes so great that all thinking is brought to a natural stop. Then just see–who is here to see?–what’s right here.