To shuffle (シャッフル shaffuru) a pile of cards is to randomize the order of the cards in that pile. Each player shuffles their deck at the beginning of the game, and whenever it is searched by effects.
Some effects instruct the player to shuffle a card(s) into their deck. To do so, that player puts that card anywhere in their deck, then shuffles their deck so that the position of the card shuffled into the deck is randomized along with the rest of the deck's contents.
Certain effects that have a player look at a number of cards from the top of their deck will have that player shuffle those cards and put them on the bottom of their deck. These effects use the phrase "shuffle the rest and put them on the bottom of your deck" in Japanese, and are denoted by "put the rest on the bottom of your deck in a random order" in the English version of WIXOSS.