How to select first parent DIV using jQuery?

Use .closest() to traverse up the DOM tree up to the specified selector.

var classes = $(this).parent().closest('div').attr('class').split(' '); // this gets the parent classes.

Use .closest(), which gets the first ancestor element that matches the given selector 'div':

var classes = $(this).closest('div').attr('class').split(' ');

EDIT:

As @Shef noted, .closest() will return the current element if it happens to be a DIV also. To take that into account, use .parent() first:

var classes = $(this).parent().closest('div').attr('class').split(' ');