1. [n]  doing or saying again; a repeated performance
2. [n]  (computer science) executing the same set of instructions a given number of times or until a specified result is obtained; "the solution is obtained by iteration"
3. [n]  (computer science) a single execution of a set of instructions that are to be repeated; "the solution took hundreds of iterations"

Repetition of a sequence of instructions. A fundamental part of many algorithms. Iteration is characterised by a set of initial conditions, an iterative step and a termination condition.

A well known example of iteration in mathematics is Newton-Raphson iteration. Iteration in programs is expressed using loops, e.g. in c:

        new_x = n/2;
        do
        x = new_x;
          new_x = 0.5 * while (abs(new_x-x) > epsilon);

Iteration can be expressed in functional languages using recursion:

        solve x n = if abs(new_x-x) > epsilon
                    then solve new_x n
                    else new_x
                    where new_x = 0.5 * (x + n/x)
        solve n/2 n