Often when a builder has no obvious work he will start to fix a hut. As you've discovered, dropping a villager on a completed hut will also set them fixing it. If he is successful he will gain some building skill, as mentioned by Barbara.

However, you've got to make sure the villager is "fixing" the hut. If he's just "examining" it he won't gain any skill. In those cases I'll drag him away and re-drop him until the status bar shows he is "fixing".