Plug is a term that refers to a group of cards separated by plastic cut cards. The term is most often used in casino games played with multiple decks, such as blackjack, for example.
As you may know, to prevent players from counting cards, casinos often use multiple decks of cards for blackjack that are then placed in a device that holds all those decks, which is known as the shoe. One cut card is inserted at the end of the shoe to prevent the players from seeing the last card in the shoe, while the other cut card is used to separate the discarded cards from the un-played cards. In a way, the two cut cards plug the deck, hence the name.
The time needed to reshuffle the cards can vary from one casino to another, but before re-shuffling, the dealer will simply look at the position of the cut cards and know what portion of the decks to re-shuffle.