The delta would be the "raw" form of the direction and corresponds exactly to the vector (107, -23) oNyx pointed out. To normalize a vector means to divide this vector, so that the line you draw along this direction is exactly of the length 1, meaning dividing the x/y delta values by the overall lenght of your "raw" direction. You can calculate this using the formula of pythagoras: double len=Math.sqrt(Math.pow(x,2)+Math.pow(y,2)).
Normalizing the direction vector has the advantage of representing the x and y deltas you need to travel 1 unit in the desired direction.
A decent vector library can take away the details of such operations and offers the benefit of easy transition from 2D graphics to 3D graphics, so I would suggest to get some reading on linear algebra and vector math in detail. I can recommend the book "Essential Mathematics for Games and Interactive Applications"http://www.amazon.com/gp/product/155860863X/qid=1134564195/sr=8-2/ref=sr_8_xs_ap_i2_xgl14/002-9312530-3104828?n=507846&s=books&v=glance
but it might be a bit much to swollow (700 pages, but it includes nearly all game related mathematics needed)