The concept of a function is vital to math, computer programming, and engineering - but it can easily be extrapolated to cover any aspect of life. A simple definition of "function" is a thing that provides a consistent output, wholly dependent on the set of inputs it's given.
A function is a relation between sets that associates to every element of a first set exactly one element of the second set.
In all domains of use, functions are sometimes named and sometimes not. Mathematical functions can be referred to by their algorithm, such as:
$$ f(x) = 2x + 1 $$
Or, for well-known algorithms, by a name - such as:
The Quadratic Formula
The inputs to the function.
The whole set of possible inputs for each argument.
The whole set of possible outputs.
The number of arguments the function depends on to produce its result.
The result of a function. Its output.