A postcondition of an algorithm is a logical statement that must be true after the algorithm executes. That is, it defines what the algorithm does.
Take, for example, our sqrt function
real sqrt(real x)
real t = x
while abs(t - x/t) > 1e-15 * t
t = (c/t + t) / 2
return t
which has the postcondition that the return value,
multiplied by itself,
will evaluate to the parameter;
that is, ret * ret = x.
(Note that we use ret to denote the return value.)
If a function's preconditions are satisfied, not satisfying a postcondition is a defect in the algorithm or its implementation. Postconditions are generally tested via unit tests, which it is the responsibility of the algorithm implementor to provide.
A suitably paranoid caller could, of course, also verify postconditions, but that should never be necessary.