that在这里是个代词 代指function 这句话的意思是...的功能和Judge的功能是相似的.
如果还原成原句的话就是 His function is analogous to the function of a judge.
语法：
that和those在一些句型中可以代替前面的名词以避免重复
The Weather in Beijing is hotter than that in Heilongjiang in summer.
在夏天北京的天气要比黑龙江的天气热.
The books in our school library are more than those in yours.
我们学校图书馆的书比你们学校的多.