The right aortic arch normally disappears during fetal development, but sometimes this blood vessel remains and puts pressure on the esophagus. This pressure makes swallowing difficult, so food may build up in the esophagus, stretching it and making it big, hence the name megaesophagus. Your veterinarian will see a dilation of the esophagus above the heart and a constriction at the base of the heart. Treatment is surgery. The more time that passes without surgical correction, the more the esophagus stretches, causing permanent damage and decreasing chances of the esophagus ever becoming normal.
Foreign bodies can have the same effect.
Imagine a tortilla chip stuck in your esophagus. It may cause pressure or perforate the esophagus. A fibrous scar in the esophagus may ensue, leaving a stricture that can cause megaesophagus. Tumors in the esophagus may form an obstruction as well. Again, surgery is usually necessary.