The two definitions are right there in the photo you posted 2.3.1
Try reading it again and look at the examples provided.
The first f(x,y,z) adds up a bunch of Boolean terms. Each term is composed of factors of x,y and z. X,y and z can have values of 0 or 1 so each term is an AND of x,y and z. The adding is in reality the OR operation.
The equation is saying f(x,y,z) is true when xyz is true OR x'yz is true OR ... That's a minterm way of defining the f function.
The alternate way to define the f function is to use a product of factors with each factor being an OR of x, y, z inputs.