Structures are a type of card that represents pretty much any big structure that can be built by the player. It's icon is a Minecraft brick. They have a certain amount of HP (health points) that when depleted to 0, the card is discarded, and a resource requirement which must be paid by tapping resource cards of that kind to put the card in play. They're played on the Village between your Player and the Battle Front which holds your Mobs.
Contrary to popular belief, not all Structure cards protect the player - only those with the Shelter ability do, but cards like Bomb Shelter protect the player through other ways - in the case of the card, by nullifying any attacks of Creepers and TNT cards.