Meaning of repeated "什么"
什么什么 can be used as a filler like "blabla". In Japanese the pedant is used (何). Good translations would be "and so on" or "blabla", imo.

Example, when trying to explain how "As soon as" works in Chinese:


  "他一什么什么，他就做什么什么。。。"


--> This is the generic version of the usage of "as soon as".

I would translate this with 


  "As soon as he [...], he makes/does [...]" 


whereas the [...] is filled by 什么什么 and in English this could be "blablabla": 


  "As soon as he blablabla, he makes/does blablabla".


Source: My own experience as a non native speaker and my wife (who is a native speaker and whom I am going to ask today evening to confirm my answer)

EDIT: I asked her, she can confirm my answer. But there also is another usage of repeated 什么:
Your question refers to "那什么什么" - which is used as a substitution, in  case you forget a word during a conversation. So instead of saying the name of the thing you use "那什么什么". 

Interestingly, a similar concept exists for persons/names. If you forgot a person's name or do not want to use the name the substitute "那谁" would be used.