Insects are incapable of "eating" concrete, but they do tend to exploit weak or damaged concrete to access something more appealing, such as a food source or nesting site.
It only takes a small crack in an otherwise secure concrete foundation to let termites in. Poured concrete is the most reliable, but if you have a block foundation, the mortar is likely to provide open spaces. Expansion joints between home sections are another invitation to pests, as is any area where pipes or wires enter the house.
Once inside, termites build dirt tunnels. These tunnels get wider over time, so even though the bugs aren’t eating your foundation, they can cause a great deal of damage as pressure builds up and widens existing cracks. This slow process may go unnoticed until it becomes serious, making regular inspection of your home and foundation an important part of pest control.
Eradication is best left to a professional for something this serious.