Why should we "eat the juice"?

In kindergarten, we learnt - “Eat the Liquid & Drink the Solid.” The real meaning is to chew your solid food till it turns into a liquid and then drink it. And keep the liquids in your mouth for a little while before swallowing it. 

When we properly chew our food, our mouth produces digestive juices in the form of saliva, which help in digesting that food. This includes the juices that we consume during the fast.