Flashback is a keyword ability that lets you cast a card from your graveyard. When a card has flashback, you can pay its flashback cost instead of its normal cost to cast it from your graveyard. After it resolves, it's exiled instead of going back to the graveyard. The reminder text puts it simply: "You may cast this card from your graveyard for its flashback cost. Then exile it."
In play, flashback turns your graveyard into a second hand. It gives you extra value from cards you've already used, letting you cast a spell twice for two different costs. This makes flashback cards flexible: you can use them early and again later. It also punishes opponents who rely on discard or mill, because those effects can actually help you. Since the card exiles after flashback, you can't loop it forever, but the one extra use is often worth it.
