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.
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.