Buyback is an ability that can be found on creatures, instants, sorcery's, and even artifacts! Introduced in the Tempest block, this ability allows you to take back a card you just played for an additional cost. However, it's an additional cost. Meaning that if you play a spell that costs 3 colorless and 2 blue, and the buyback cost is 2 colorless and 1 blue, you will have to pay a total of 5 colorless and 3 blue when adding the buyback cost in.
If this spell is countered, however, both the spell and the buyback are countered. The buyback cost only takes effect if the spell resolves, in which case it was countered, it would not have.