What exactly does Types as ranges of significance of propositional functions. In modern terminology, types are domains of predicates mean?Update:I found in this paper (Pag 14 or 234) by Russell, where he defines what is ranges of significance, not exactly including types else propositions. A function is said to be significant for the argument $x$ if it has a value for this argument. Thus we may say shortly $\phi x$ is significant,  meaning the function $\phi$ has a value for the argument $x$. The range of significance of a function consists of all the arguments for which the  function is true, together with all the arguments for which it is  false. 
The range of significance in Type Theory
type theory
I believe this is simply referring to old terminology, as the quoted text implies.When using a formula such as $\sqrt{x-5}$, it is common to specify what $x$ is intended to be so that the formula makes sense. That is, we could let $x$ to be a real number $\geq 5$, so that the square root is defined. Only when $x$ ranges over the values satisfying such condition the formula is meaningful, or has significance. Hence, the range of significance of a formula essentially is the class of the values the variables must be in so that the formula makes sense.This is true in propositions, too. If a propositional formula involves variables, as in $f(x) < 4 \implies f(x) < 0$, then we can regard the formula as a function mapping the value of its (free) variables $f,x$ to a proposition. This is why it can be called a propositional function. Its range of significance are the values $(f,x)$ which make the proposition meaningful. We can't let e.g. $f = 5$ and $x = \mathbb{N}$, so that pair is outside the range.In modern terms, indeed, this is what we usually call domain of a predicate. 