Most fractal equations involve iterating the same equation many times for the each pixel. If the coordinates you keep modifying start heading towards infinity, you can stop iterating and display the appropriate colour for the number of iterations that you did. If the coordinates never head for infinity, you can colour them with the interior colour because that means they are part of the set (Mandelbrot set, or whatever fractal you are calculating).
But how do you decide that they are never going to head for infinity? The only way to be sure is to iterate the equation an infinite number of times, a process that tends to take quite awhile! So, max. iterations specifies the threshold of your patience. A high value will produce more detailed pictures, with more iteration bands, but will take longer to calculate.
You set the max. iterations value using the Maximum Iterations Per Pixel control in the Iteration Control window.