Puffins are not good flyers, like eagles or hawks, but they fly! By travelling with Glacial Experience on a private tour you can see puffins over summer time. They have short wings and thus have to move them fast in order to move their heavy body around. During the nesting time they fly back and forth from their nest. Their nest is in a hole they dig into the ground and from the hole they fly to the sea hunting small fish they then bring to the young ones.
The reason for the question is probably the likeness between the puffins and penguins. Travelleres sometimes see the puffins as very small penguins, as well as other species of what we call "black birds", svartfuglar in Icelandic.