This is the hug where somebody goes in for a hug and there is a moment of awkwardness. You're not quite ready for the hug or are thrown off guard by the possibility of a hug happening so what do you do? You just kind of fidget and then give the other person a little arm up pat on the back. It's almost like hugging a sibling that you're not quite affectionate with so you pat each other instead.
" I ran into Joe the other day...since we haven't seen each other in years I wasn't sure what to do when he went in for a hug so I gave him The Bro-Hug instead. I'll never hear the end of it for that one!"