A
total function for which there is an
effective method of computing its output, for every input.
A computable function can also be defined as one that can be computed by an algorithm, or (equivalently), by a Turing Machine.
For example:
f(n) = n + 1 is a computable function. The algorithm that solves it takes the input and adds one. (How simple is that?)
Turing's Halting Problem is an incomputable function.