A Proxy is a fake card that is used to take the place of a real card.
Proxies cannot be used in official tournaments. They are usually used when people are testing out a new decklist that maybe they found online or from a friend. Once they test it and like how the deck runs, then they start to purchase or trade for the cards that they need. Proxies can be made by printing the real card or simply writing the name of the card, effect, type etc. on a slip of paper and placing it inside a card sleeve with a real card behind it. Proxies are a good way to test out a deck or cards before making a purchase.
Players should be mindful, though, that any duel with a proxy card should be just considered a test of a deck's potential.