I just realized I am not very comfortable with the terminology of large and small gauge transformations[ http://en.wikipedia.org/wiki/Large_gauge_transformation ]. I've done some digging around and even looked through some previous posts about this on the physics exchange.
 
It turns out to be important in string theory, and can crop up in more elementary details of Yang-Mills as per @Luboš Motl. My ignorance of this came up in a discussion on physics exchange, @Hunter comments on @user1504 answer http://physics.stackexchange.com/q/94981  and his previous inquiry in physics exchange have brought me to this point.

Clarify this difference. Can someone describe how it crops up in Quantum Yang-Mills? If perhaps one can engineer a simple physical theory that has such a transformation to describe its subtleties it would be great.

As usual I love really simple explanations as I am not any sort of expert.

I don't know if I pose the question correctly, but please feel free to edit it.