class="two-thirds columns" enforces a strong coupling between the HTML and how it is presented.

To change how wide a column is, you change its class. To change how wide an image is, you go into the CSS. To change how wide a column's border is, you go to the CSS. Doesn't changing the class seem a little out of place?

In theoretical terms, the class is semantically the category to which the component belongs. a <section class="cart"> is perfectly reasonable, whereas <div class="two-thirds columns"> is not. The <div> and it's children are not tied to the notion of how wide the div is. The fact that a section has class "cart" is important in understanding it's children.