Disable click outside of bootstrap modal area to close modal

On Options chapter, in the page you linked, you can see the backdrop option. Passing this option with value 'static' will prevent closing the modal.
As @PedroVagner pointed on comments, you also can pass {keyboard: false} to prevent closing the modal by pressing Esc.

If you opening the modal by js use:

$('#myModal').modal({backdrop: 'static', keyboard: false})  

If you are using data attributes, use:

 <button data-target="#myModal" data-toggle="modal" data-backdrop="static" data-keyboard="false">
    Launch demo modal
 </button>`

This is the easiest one

You can define your modal behavior, defining data-keyboard and data-backdrop.

<div id="modal" class="modal hide fade in" data-keyboard="false" data-backdrop="static">

You can use an attribute like this: data-backdrop="static" or with javascript:

$('#myModal').modal({
    backdrop: 'static',
    keyboard: false  // to prevent closing with Esc button (if you want this too)
})

See this answer too: Disallow twitter bootstrap modal window from closing