The counterpart (the paper bit of the UK license) details any driving convictions you may have acquired.
There's a rough equivalent to that in the US but the driver doesn't keep it, it stays with the DMV and is a centrally kept record.
Why the same thing couldn't be done in the UK, I don't know? I suppose it's easier for you to see what convictions you might have
if you committed an offense years ago and it's a bit easier for a law enforcement officer to quickly see your convictions but surely the officers
can check these things out via computer system? Or am I asking too much here? 
It's all stored on the DVLA computers, so there would be no problem at all getting the conviction details during a routine police check of driver records.
For some reason the system here also refers to those convictions as "endorsements," which has always struck me as odd. To me, an endorsement would be something like a addition to a license which says you are also licensed to drive a larger vehicle, or that the license also acts as a learner's permit for some other category of vehicle.
Before DVLA was set up in the 1970s British licenses were a small booklet containing a half dozen or so pages, stiff red covers, and somewhat smaller in overall dimensions than a credit card. I still have one which was my mother's, issued in the 1960s and carrying renewal stamps up to 1972.
When DVLA came on the scene, they went to the computer-printed wallpaper. First it was a giant green sheet of paper, then the format was messed around and it was a pink sheet, then they changed to a common European format (supposedly) which was green
and pink (Ugh!), and now finally we have the photocard with counterpart.
Edit: Thinking about it some more, it might have been pink first, then green. I know I've had all three variations of pink, green, and pink/green over the last 22 years.
