Looking at page 3 of the book linked, the author is using "type" in the philosophical sense, not the mathematical sense. This "type-token distinction" is a topic that gets a lot of attention in philosophy, but most books on mathematical logic don't discuss it, because we can get by for a long time without worrying very much about it, and because the time it takes to discuss it properly would take time and energy away from the mathematics.
The general idea is that there is some collection of abstract "types" of things. For example, there is a type of "bicycles" and a type of "apples". Then there are specific bicycles - each of which is a "token" of the type of bicycles, and there are specific apples, which are tokens of the type of "apples". This should sound vaguely like something from Plato.
Similarly, there is a type of "the string 101". Each time I write down "101", I write down only a token of the string. So 101, 101, and 101 are three different tokens of the same string.
In philosophy, the question "what is a type, really?" has received a lot of discussion, as you might imagine. But that question is not particularly important to the direct study of mathematics, we can do a lot of math without ever worrying about it.
One place that the type/token distinction does arise in logic is with occurrences of variables. Consider the sentence of first-order logic
R(x) \land (\exists x) [P(x)]
Here there is only one variable, "x" - so a variable is a type. There are two occurrences (tokens) of the variable, though (three if we count "$(\exists x)$"). One of them is in the scope of a quantifier, and the other is not. This distinction between "variables" and "occurrences of variables" is quite important for understanding the concept of free and bound variables.
In the field of type theory (and computer programming) there is a somewhat related idea of the type of a variable. In these systems, every variable has a "type" associated with it, and the type of the variable dictates what can be done with the variable. For example, in one system I have a type of natural numbers and a type of sets of natural numbers. If I have two numbers, I can add them. If I have a number and a set, I can ask whether the number is an element of the set. But, in this typed system, I cannot add two sets or ask whether a number is an element of another number, because those operations don't match those types. Most first-order logic is done in a non-typed way (so there is only one type of variable).
So do you need to worry about the type-token distinction for propositional logic as a student learning it for the first time? If you are interested in the philosophical aspects of the subject, then you certainly do. If you are only interested in the purely mathematical relationships between the formulas of the logic, and less about the applications of the logic to philosophy, then you may be able to get by, as many texts do, using some common sense but otherwise not spending too much time distinguishing types from tokens.