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Array iteration is the process of sequentially accessing each element within an array to perform some operation. In programming, arrays are collections that hold a fixed number of values of the same type, and they are stored in contiguous memory locations. When you need to calculate the total value of an array, you must iterate through each of these values one by one.

During array iteration, you typically use a counter variable that starts at the index of the first element, often 0, and increments by one until it reaches the last index of the array. It's crucial to ensure that this process accounts for every element by accurately setting the termination condition of the iteration, thus preventing any form of under or overreach within the array's bounds.

The for loop is a control flow statement used in various programming languages to iterate over a range, collection, or sequence of elements. It is particularly helpful in the scenario of processing each item in an array. A for loop is constructed with an initializer, a condition, and an increment expression.

For example, to iterate through an array containing integers, you could initialize the loop with a counter at 0, continue the loop as long as the counter is less than the array's length, and increment the counter after processing each element. This pattern makes the for loop a fundamental tool in working with arrays, as it neatly aligns with the array's indexed nature.

When adding together all the elements in an array, known as summing, you carry out a repetitive operation that accumulates values. Starting with a total sum of 0, each element's value is added to this total as you iterate through the array.

For clarity, if you have an array with the elements \( [1, 2, 3] \), the summing process would be: start with a total of 0, add the first element to get 1, then add the second to get 3, and finally add the third to get 6. Thus, the sum of the elements in this array would be 6. By maintaining a running total, you can keep track of the aggregation without the need for additional arrays or complex structures.

Programming logic involves the sequence of instructions and decisions made to achieve a desired output from a given input. In the context of summing array elements, logic is used to control the flow of the program to ensure that each element is properly accessed and accounted for in the sum.

Good programming logic dictates that the solution be efficient and cover potential edge cases, such as empty arrays or non-numeric elements. By using conditional statements, loops, and a clear understanding of data structures like arrays, a programmer can craft an elegant and robust solution to summing array elements.