What is the command of output superfunction in mathematica?

I have two questions:

1. What is the command for a superfunction in Mathematica?
2. What is the difference between above superfunction and function in superspace which is odd variables times ordinary function? Are they the same thing?

In wikipedia, a superfunction S(z) of f is defined as S(z)=f(f(f(...f(t)))) (z total f's).

At 1: The command you're probably looking for is Nest:

In[1]:= Nest[f, x, 3]

Out[1]= f[f[f[x]]]

At 2: This doesn't look like a question for the Mathematica tag. It seems more physics/math related. I have added tags accordingly.

To address part 2 of your question:

Besides the prefix super-, there is no relation between superfunction (meaning an iterated function) and functions in super vector spaces.

Also, a superfunction is normally defined to be a map from a superspace to a supernumber, it does not have to be an odd element as stated in your question. See, e.g., section 1.10 of Ideas and methods of supersymmetry and supergravity.