Understanding nested for loops in javascript

var arr = [[1,2], [3,4], [5,6]];

This is an array of arrays. It is a little bit easier to read like this:

var arr = [
            [1,2],
            [3,4],
            [5,6]
          ];

That makes it a little bit easier to see that you have an array of 3 arrays. The outer 'for' will loop through each of 1st level arrays. So the very first outer for loop when i=0 you are going to grab the first inner array [1,2]:

for (var i=0; i < arr.length; i++) {
    //First time through i=0 so arr[i]=[1,2];
}

In the inner loop you are going to loop through each of the 3 inner arrays one at a time.

for (var j=0; j < arr[i].length; j++) {
    //Handle inner array.
}

This argument grabs the length of the inner array:

arr[i].length

So on your first time through the outer loop i=0 and arr[i] is going to equal [1,2] because you are grabbing the 0th element. Remember, arrays elements are always counted starting at 0, not 1.

Finally you are printing out the results with:

console.log(arr[i][j]);

The first time through you can break it down a little. i=0 and j=0. arr[0][0] which translates as grab the first element from the outer array and then the first element from the first inner array. In this case it is '1':

[
    [1,2], <-- 0
    [3,4], <-- 1
    [5,6]  <-- 2
];

The code will loop through the first first set [1,2], then the second [3,4], and so on.

The double for loop you have above works like so:

 var arr = [[1,2], [3,4], [5,6]];

 for (var i=0; i < arr.length; i++) {
  // i = 0, then we loop below:
  for (var j=0; j < arr[i].length; j++) {
    //here we loop through the array which is in the main array
    //in the first case, i = 0, j = 1, then we loop again, i = 0, j = 1
    console.log(arr[i][j]);
    //after we finish the stuff in the 'j' loop we go back to the 'i' loop 
    //and here i = 1, then we go down again, i, remains at 1, and j = 0, then j = 1
    //....rinse and repeat, 
  }
}

In plain english:

We grab the first element in the main array, which is an array itself, we loop through that, and log at each index, this is terminated by our length condition in the second loop. We then move to to the next index of the main array, which is an array itself.... and so on, until we reach the end of the main array

To access and index in the main array, we need to use array[i] - that index holds an array - so to go INTO that array, we need to use array[i][j]

Hope that makes sense!