Gi and no Gi are the two forms of Brazilian Jiu-Jitsu. Gi Jiu-Jitsu is grappling with the use of a traditional Gi, which allows you to grab the clothing of your opponent. NoGi is grappling without the traditional uniform, instead you wear shorts, leggings, spats and a rash guard or shirt. In NoGi you cannot grab your opponent's clothing. While this sounds like a hinderance not being able to grab your opponents clothes, it does open up submissions that are usually banned in the Gi or some Gi Competitions, such as reaps, heel hooks etc.
Highlight clip of the Black Belt Adult Male Absolute Competition @ IBJJF Worlds