When you construct something again, you rebuild it. If the chair you made from scraps of wood collapses when you sit in it, you can either rebuild it or give up on the idea of making your own furniture.
When a natural disaster — like a hurricane or a tornado — destroys people's houses, they usually need the community's help to rebuild them. Before modern fire departments existed, several cities in the United States burned in terrible fires, destroying nearly all the homes and businesses. These cities had to rebuild, which they often did using less flammable materials, like bricks, rather than just wood.