Barium is a substance that shows up on x-ray and a barium meal is when your child would swallow some liquid or solid containing barium and we would watch it go into the stomach, and then the intestine, and follow this through the intestine.
It is very helpful to look for anatomical/structural abnormalities which may cause reflux, vomiting, feeding difficulties, abdominal pain, bloating for example.
Even though it does involve some radiation, it is a very useful test in the right circumstances.