The modern technical definition of a functional is a function from a vector space into the scalar field. For example, finding the length of a vector is a (non-linear) functional, or taking a vector and returning the 3rd coordinate (relative to some basis) is a (linear) functional.
But in a classical sense, functional is an antiquated term for a function that takes a function as input. For example, the function
derivativeAt(p)(_) that takes a function f and returns f'(p) is a functional in the classical sense, as well as the function
integralOver(a,b)(_) that takes a function f and returns the integral of f on [a, b].
Today, we'd call these higher-order functions in a Comp Sci setting, but in a Math setting we typically take to just calling them functions, or colloquially functionals in order to distinguish them from the other functions we are working with at the moment. I suspect that your statistics text might be using this classical version of the term colloquially.