If you are referring to the picture at the bottom of this post:
http://www.winestoragebuzz.com/traveling-with-wine/
That’s not an image border, it’s a caption background. If you type something in the “caption” box when you upload the photograph, that’s what you’ll get.
You can style that using code like this:
wp-caption {background: none;}
or
wp-caption {background: #C89D9D;}
(Gives you something that goes with your theme colors. Got it from this page: http://www.w3schools.com/tags/ref_colorpicker.asp?colorhex=%23750B0B)