Building is a game mechanic which is used for creating Buildings. It acts very similar to harvesting - once a Build Site is available, either double tapping it, dragging a Dragon with Stamina into it or a Dragon choosing it randomly, will initiate the building process.
The Dragons will "jump" up and down when building while the Build Site's sprite will highlight with every "jump", in addition to building sounds. More Dragons can be called to the Build Site in order to speed up the process.
It is worth noting that once a Dragon starts to build something, its Stamina is instantly decreased by one, whether it completed the Building or not, meaning that if a Dragon is moved back and forth from a building Site, it will effectively deplete all of its Stamina rather quickly, with the Build Site not turning into a Building at all. This is happening because in contrary to harvesting, the building bar wouldn't reset if the building process is halted, but rather be accumulated. Do note that a building Site can be build with 1 Stamina of any Dragon, even the weakest, though it would take longer the weaker the Dragon.