Dredge: Dredge is a static ability that functions only while the card with dredge is in a player's graveyard. "Dredge N" means "As long as you have at least N cards in your library, if you would draw a card, you may instead put N cards from the top of your library into your graveyard and return this card from your graveyard to your hand." A player with fewer cards in his or her library than the number required by a dredge ability can't put any of them into his or her graveyard this way. See rule 502.47, "Dredge."
If they have a card in their graveyard with dredge, instead of drawing (as a replacement effect, so you can't respond to it), they can mill cards from their library equal to the dredge cost of the card, and then put that card into their hand.
The deck works by dredging to put every card from their library into their graveyard, put Narcomeobas and Ichorids into play, disrupt the opponent with Cabal Therapy, and flashback Dread Return to put Flamekin Zealot into play and win. It works well with Bridge from Below.
(Looking up those cards with elucidate things).