原汤化原食 is a kind of eating habit, especially exists in northern areas; means drinking the soup of the dumplings (or noodles etc) after eating them. e.g. for the case of dumplings, 原汤 refers to the water (or you can think it as soup) which used for boiling dumplings, 原食 means dumplings.
(In general, 原食 refers to starchy foods, like dumplings, noodles, wontons, glue puddings etc, 原汤 refers to the water which used for boiling these foods. 化 means digestion, so 原汤化原食 means the soup could help digesting starchy foods.)
There're several various explanations about why people doing this, someone believe 原汤 could help digestion; someone believe 原汤 is nourishing. I prefer to that it's just a habit; people like drinking something after eating and with 原汤 you don't need to cook the soup separately. And I think this article gave a nice summary: