It is one of the concepts used in "ON THE REPRESENTATION OF CONTINUOUS FUNCTIONS OF SEVERAL VARIABLES AS SUPERPOSITIONS OF CONTINUOUS FUNCTIONS OF A SMALLER NUMBER OF VARIABLES", in the second paragraph, highlighted with black background,
[as shown in this image](https://i.stack.imgur.com/7vbus.png).



What does "a universal tree" mean?
In the beginning of Section 6 on p. 318 of Menger's Kurventheorie, referred to in [Kolmogorov's paper](https://cs.uwaterloo.ca/%7Ey328yu/classics/Kolmogorov56.pdf) on the page whose image you linked in your post, we find this:



> 
> Wir bezeichen eine Baumkurve $B$ als einen Universalbaum bzw. als Universalbaum $n$-ter Ordnung, wenn $B$ zu jedem vorgelegten Baum bzw. zu jedem vorgelegten Baum $n$-ter Ordnung eine homöomorphe Menge als Teilmenge enthält.
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> 


which apparently means



> 
> We refer to a tree curve $B$ as a universal tree, or a universal tree of the $n$th order, if $B$ contains as a subset a homeomorphic image of any given tree, or any given tree of the $n$th order.
> 
> 
> 


