The term used to describe when someone has one sleeve rolled, pulled up, or even ripped off, while the other sleeve is left intact. Also, weird shirts that have only one sleeve by design.
If you are planning on beating someone up and only using one arm in doing so, then gangster sleeves might be useful so that you don't give your adversary (opponent) a faceful of fabric.
Amputees with only one arm might be said to have gangster sleeves, though that seems a tad bit disrespectful, and it's advised against using the term in this situation.
"That idiot just ripped my sleeve off... now everyone's gonna say I've got those damn gangster sleeves!"
"OH EM GEE, Julia, gangster sleeves are so IN right now, I have to buy 50 million shirts that have them!1!1!! one one one!"