When counting through a list, or cycling through a loop, each iteration has a place. There is the first iteration, the second, the third, the fourth, and so on. The final iteration is the nth iteration, commonly. The count of an arbitrary iteration is the ith.
This nomenclature exists, most likely, in classrooms composed of bored students - I've heard it used both in highschool math class and in university CS courses. The term is derived, I believe, from a typical loop form, namely:
for(i=1; i<n; i++)
In plain language the above says to iterate through the loop until 'i' is less than 'n'. Start with 'i' being one, and increment 'i' each time. In plainer language, loop 'n' times (assuming 'n' is a positive, finite integer).
Now to describe what happens in a specific iteration (in an argument for the correctness of whatever is inside the loop, perhaps), how would you name it? As you enter the loop at the begining, you are performing the first. The last time you test 'i' and 'n', you are preparing to start the nth. And the 'general' iteration through the loop, when you do not care what 'i' is, knowing that it is not the first or the last? That is the ith iteration.