From the Super Mario Wiki
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Huffin' Puffins (also formatted as Huffin Puffin) are strange puffin-like birds that appear in a few levels of Super Mario World 2: Yoshi's Island and Yoshi's Island: Super Mario Advance 3. They're always in a group of one parent and a couple of juveniles. If Yoshi hits the mother, she will run in the opposite direction, and Yoshi is able to take the children. They act the same as Eggs, so Yoshi can pick them up by walking into them. If Yoshi loses one, he can return to the area where the mother is walking to claim more. Sometimes if the Huffin Puffin chick throw is cancelled, they attempt to run away.
The young ones are extremely useful, as when Yoshi throws one, it circles about in boomerang fashion, eventually returning. It can only hit a surface three times, any more and it falls off the screen. When Yoshi jumps through the goal at the end of the level, the puffin kids will fly away.
The Huffin' Puffin family returns in Yoshi's Story. They are only found in Stage 1-2: Surprise!! and Stage 3-4: Frustration. They act exactly like they did in Super Mario World 2: Yoshi's Island. The Baby Yoshis growl at the Huffin' Puffin as if it were an enemy. This could be because they have never seen a Huffin Puffin and are not certain if they're friend or foe.
Huffin' Puffin and its children make a small cameo in Mario Party Advance. In Bowser Lab, Bowser and Koopa Kid will ask the player what kind of opponent they want to face in a duel minigame, if the player chooses "A very scary monster," Huffin' Puffin will appear out of nowhere, simply say "Huffin' Puffin" and walk away. Bowser will then chastise the player and say next time they should just challenge "A scary monster". The game's end credits say Huffin' Puffin disappeared and that not even Bowser knows where it went.
Huffin' Puffins reappear in Yoshi's Woolly World, acting differently this time and renamed Fluffin' Puffins. The adult Fluffin' Puffins can be destroyed, whilst the Fluffin' Puffin chicks were redesigned and no longer come back when thrown; instead, they create a fluffy, cloud-like platform that follows their movement.
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