These creatures smell blood in the air, they come into play bigger than normal if damage was dealt to the opponent that turn.

702.51. Bloodthirst

• 702.51a. Bloodthirst is a static ability. "Bloodthirst N" means "If an opponent was dealt damage this turn, this permanent comes into play with N +1/+1 counters on it."
• 702.51b. "Bloodthirst X" is a special form of bloodthirst. "Bloodthirst X" means "This permanent comes into play with X +1/+1 counters on it, where X is the total damage your opponents have been dealt this turn."
• 702.51c. If an object has multiple instances of bloodthirst, each applies separately.

Rules Translation

• 702.51a. - This is an always active ability checking if damage was dealt to the opponent if so and the permanent comes into play then it comes into play with N +1/+1 counters where N equals the number following Bloodthirst.
• 702.51b. - Normally it's on the card as Bloodthirst [number] but there is also Bloodthirst X and this means that the creature comes into play with +1/+1 tokens equal to the total damage dealt to all opponents this turn.
• 702.51c. - Bloodthirst stacks and so is applied multiple times.