The functions f, g and h are just given. The fundamental idea of a function is that it is some way of converting an input into an output. Writing an expression with "and", "or" and "not" is just one way to define a Boolean function. We can use any means as long as it guarantees that every possible input is connected to a single output. In this case, f, g and h are given by explicitly listing their values for each input. The text says, "Let's consider these particular functions". Now, it turns out that every Boolean function can be specified by a Boolean expression, as in this example. This is not the case for functions on real numbers or even natural numbers. For example, the function that, given the coefficients a4, ..., a0 of a polynomial x5 + a4x4 + ... + a0 of degree 5 returns the smallest root of this polynomial cannot be expressed using the four arithmetical operations and roots.