"Av" or "Aperture Priority" mode is one where you set the aperture (f #) and the camera set's an appropriate shutter speed. This mode is generally used when you want to control the depth of field (DoF) or amount of the image that's in sharp focus. Most modern DSLRs can also have 'Auto ISO' enabled in almost any mode, so you could have had the camera setting both aperture and ISO.
With respect to the missed focus, if you look at the hair immediately above the lad's shoulder nearest the back, it's relatively sharp, while the face is quite soft or out of focus. This tells me that the camera chose to focus on the hair at the back of his head, for whatever reason, rendering the face unfocused; not generally desirable in portraits. My preference for shooting portraits of any sort (in fact for almost all photography really) is to use a single AF point and place it where I want the area of critical focus. Allowing the camera to decide without verifying what it's focused on will often lead to less than desirable results, as in this case.