If you want to receive focus on a <div>, <li>, or another element like these, you must set the tabindex attribute on that element. Otherwise, the focus handler won't be called. I usually set the tabindex to zero since I don't want the user to <tab> to the element.
Below is some example code to demonstrate this. I wrote a simple HTML page with a <div>, and used jQuery to setup the focus event handler.
You can download the example or copy the code below.
What does the example look like?
The tabindex is set in the HTML below, and the alert is seen when you click on the <div>. If you remove the tabindex attribute, the focus handler will not be called.