Javascript run a function inside a loop every x iterations

Create a second variable which keeps hold of the current count, then wrap the call you only want every third iteration with

if(counter % a == 0) {
    //code you want called
}

Well firstly you will need an incrementing variable counting how many times the function has been called. For instance, start your function with this:

var me = arguments.callee;
me.timesCalled = (me.timesCalled || 0)+1;

Now, you can check that counter. To see that something happens "every X times", simply check to see if the modulus by X is 0:

if( me.timesCalled % a == 0) { /* do something */ }

And there you have it!

Here's an approach that encapsulates the counter, but uses a global variable for "a":

var a = 3;

function anim(){
    // Run the usual code here
    // ...

    if (++anim.counter % a === 0) {
        // Run the special code here
        // ...
    }
}
// Initialize static properties.
anim.counter = 0;

And here's an approach that encapsulates the "a" variable as well, referring to it as "frequency":

function anim(){
    // Run the usual code here
    // ...

    if (++anim.counter % anim.frequency === 0) {
        // Run the special code here
        // ...
    }
}
// Initialize static properties.
anim.counter = 0;
anim.frequency = 1;

Then set the desired frequency value before calling anim() for the first time:

anim.frequency = 3;

You should check that your counter is greater than 0, or your function appendEnd will be fired the first time:

if (counter > 0 && counter % a == 0) { ... }

In the following, the complete code:

var appendEndExecutedTimes = 0;

function anim(){
        left = parseInt(galleryInner.css('left'), 10);   
        if(Math.abs(left) >= (galleryItem.length * galleryItem.width())){
            galleryInner.css('left', 0);
        }
        galleryInner.animate({left: '-=20' }, 200, anim);


        if (appendEndExecutedTimes > 0 && appendEndExecutedTimes % a === 0) {
           that.appendEnd();
        }
        appendEndExecutedTimes += 1;

    }