They discovered Herculaneum while digging to lay a foundation for a royal palace, and they quickly began looking for other cities that had been buried.
" To lay a foundation" means to put usually concrete or some sort of stone on the ground, and usually underneath the ground, to support the house, to support the weight of the house.
24 huge square steel cages were pushed into the riverbed, brave divers dug out the clay and gravel in dangerous conditions to create a chamber in which concrete could be laid to build the foundations for the two towers.