"Small dining table" (xiao fan zhuo in Chinese) is a commonly accepted name for lunch services provided by schools, communities or private homes for primary and middle school students who live far away from schools or whose parents are too busy to prepare lunch. 

“小饭桌”指学校、社区或者居民家庭为离家远或者父母无暇准备午餐的中小学生提供的午餐服务。

The business quite probably started from setting up a dining table and cooking some lunch for those students. That's why it is called "small dining table". 

这门生意很可能就是从支起一张餐桌、给孩子们做顿午饭开始的，所以才会有“小饭桌”这个名字。

As business grows, their services expand too. Nowadays, a typical "small dining table" provides not only lunch services, but also after school pickup and tutoring. 

随着餐桌生意扩大，他们提供的服务也增加了。如今，“小饭桌”提供的常规服务除了午餐以外，还有放学接孩子，以及功课辅导等。