The typical CSS "box model" (also known as content-box) will produce something like this:
width + padding + border = total/visible width of box
height + padding + border = total/visible height of box
Lets look at the example div below, with the typical box-sizing: content-box.
div {
width: 240px;
height: 240px;
padding: 20px;
border: 10px solid #fff;
}

In this case the padding and border will apply to the outside producing at total visible width of 300px (240px + 40px + 20px). We'd usually need to reduce the width of the box until everything fits just right.
Or we can add this little bit of magic and it will change that altogether!
* {
-webkit-box-sizing: border-box; /* safari, chrome */
-moz-box-sizing: border-box; /* firefox */
box-sizing: border-box; /* ie8+, opera */
}

With the box-sizing CSS3 property, the padding and border will now be inside the width of the box.
This is especially useful when you are floating divs and want to give them a width (33% for example) with padding and border. Now they will all be side-by-side, taking the entire width of the parent div.