Cost synergies often involve reducing or eliminating a specific cost. For example, the combined company will not need two headquarters, so eliminating a headquarters is one source of cost savings. This might involve saving costs on salaries and rent.
Cost synergies can also come from having more bargaining power. Being a larger company allows you to get better deals on your goods and supplies, therefore reducing your cost of goods sold.
Finally, cost synergies can come from economies of scale. Being a larger company allows you to spread fixed costs such as PP&E over a larger variable cost base. In other words, a smaller % of your revenue needs to be allocated to fixed costs as you get bigger, which will improve your EBITDA margins.